Mixing
Find area of the fourth triangle given the area of three triangles.
$begingroup$
This is the question that I got in TCS Ninja under the Quantitative section.
How shall I do this? Help !!
area
asked Jan 20 at 11:03
jayjay
1034
$endgroup$
add a comment |
$begingroup$
This is the question that I got in TCS Ninja under the Quantitative section.
How shall I do this? Help !!
area
asked Jan 20 at 11:03
jayjay
1034
$endgroup$
add a comment |
$begingroup$
This is the question that I got in TCS Ninja under the Quantitative section.
How shall I do this? Help !!
area
asked Jan 20 at 11:03
jayjay
1034
$endgroup$
This is the question that I got in TCS Ninja under the Quantitative section.
How shall I do this? Help !!
area
area
asked Jan 20 at 11:03
jayjay
1034
asked Jan 20 at 11:03
jayjay
1034
asked Jan 20 at 11:03
jayjay
1034
asked Jan 20 at 11:03
jayjay
1034
asked Jan 20 at 11:03
jayjay
1034
1034
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Denote by $[...]$ the area of the polygon $...$
Lema 1
Let $ABCD$ be a rectangle a $P$ a point inside as shown. It follows that $$[APB]+[DPC]=[APD]+[CPB]$$
Proof
Draw the parallels to $AD$ and $AB$ through $P$. Then
$$[APB]+[DPC]=frac{AB·FP}{2}+frac{DC·EP}{2}=frac{AB·FP+AB·DC}{2}=frac{AB·EF}{2}=frac{[ABCD]}{2}$$
Now back to your problem $$A1+A3=2040=A2+A4=1057+A4iff A4=2040-1057=983$$
answered Jan 20 at 12:21
Dr. MathvaDr. Mathva
2,094324
$endgroup$
add a comment |
$begingroup$
Hint:
Prove that $A_1+A_3=A_2+A_4=frac{1}{2}(A_1+A_2+A_3+A_4)$
answered Jan 20 at 11:39
LarryLarry
2,41331129
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3080439%2ffind-area-of-the-fourth-triangle-given-the-area-of-three-triangles%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Denote by $[...]$ the area of the polygon $...$
Lema 1
Let $ABCD$ be a rectangle a $P$ a point inside as shown. It follows that $$[APB]+[DPC]=[APD]+[CPB]$$
Proof
Draw the parallels to $AD$ and $AB$ through $P$. Then
$$[APB]+[DPC]=frac{AB·FP}{2}+frac{DC·EP}{2}=frac{AB·FP+AB·DC}{2}=frac{AB·EF}{2}=frac{[ABCD]}{2}$$
Now back to your problem $$A1+A3=2040=A2+A4=1057+A4iff A4=2040-1057=983$$
answered Jan 20 at 12:21
Dr. MathvaDr. Mathva
2,094324
$endgroup$
add a comment |
$begingroup$
Denote by $[...]$ the area of the polygon $...$
Lema 1
Let $ABCD$ be a rectangle a $P$ a point inside as shown. It follows that $$[APB]+[DPC]=[APD]+[CPB]$$
Proof
Draw the parallels to $AD$ and $AB$ through $P$. Then
$$[APB]+[DPC]=frac{AB·FP}{2}+frac{DC·EP}{2}=frac{AB·FP+AB·DC}{2}=frac{AB·EF}{2}=frac{[ABCD]}{2}$$
Now back to your problem $$A1+A3=2040=A2+A4=1057+A4iff A4=2040-1057=983$$
answered Jan 20 at 12:21
Dr. MathvaDr. Mathva
2,094324
$endgroup$
add a comment |
$begingroup$
Denote by $[...]$ the area of the polygon $...$
Lema 1
Let $ABCD$ be a rectangle a $P$ a point inside as shown. It follows that $$[APB]+[DPC]=[APD]+[CPB]$$
Proof
Draw the parallels to $AD$ and $AB$ through $P$. Then
$$[APB]+[DPC]=frac{AB·FP}{2}+frac{DC·EP}{2}=frac{AB·FP+AB·DC}{2}=frac{AB·EF}{2}=frac{[ABCD]}{2}$$
Now back to your problem $$A1+A3=2040=A2+A4=1057+A4iff A4=2040-1057=983$$
answered Jan 20 at 12:21
Dr. MathvaDr. Mathva
2,094324
$endgroup$
Denote by $[...]$ the area of the polygon $...$
Lema 1
Let $ABCD$ be a rectangle a $P$ a point inside as shown. It follows that $$[APB]+[DPC]=[APD]+[CPB]$$
Proof
Draw the parallels to $AD$ and $AB$ through $P$. Then
$$[APB]+[DPC]=frac{AB·FP}{2}+frac{DC·EP}{2}=frac{AB·FP+AB·DC}{2}=frac{AB·EF}{2}=frac{[ABCD]}{2}$$
Now back to your problem $$A1+A3=2040=A2+A4=1057+A4iff A4=2040-1057=983$$
answered Jan 20 at 12:21
Dr. MathvaDr. Mathva
2,094324
answered Jan 20 at 12:21
Dr. MathvaDr. Mathva
2,094324
answered Jan 20 at 12:21
Dr. MathvaDr. Mathva
2,094324
answered Jan 20 at 12:21
Dr. MathvaDr. Mathva
2,094324
2,094324
add a comment |
add a comment |
$begingroup$
Hint:
Prove that $A_1+A_3=A_2+A_4=frac{1}{2}(A_1+A_2+A_3+A_4)$
answered Jan 20 at 11:39
LarryLarry
2,41331129
$endgroup$
add a comment |
$begingroup$
Hint:
Prove that $A_1+A_3=A_2+A_4=frac{1}{2}(A_1+A_2+A_3+A_4)$
answered Jan 20 at 11:39
LarryLarry
2,41331129
$endgroup$
add a comment |
$begingroup$
Hint:
Prove that $A_1+A_3=A_2+A_4=frac{1}{2}(A_1+A_2+A_3+A_4)$
answered Jan 20 at 11:39
LarryLarry
2,41331129
$endgroup$
Hint:
Prove that $A_1+A_3=A_2+A_4=frac{1}{2}(A_1+A_2+A_3+A_4)$
answered Jan 20 at 11:39
LarryLarry
2,41331129
answered Jan 20 at 11:39
LarryLarry
2,41331129
answered Jan 20 at 11:39
LarryLarry
2,41331129
answered Jan 20 at 11:39
LarryLarry
2,41331129
2,41331129
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3080439%2ffind-area-of-the-fourth-triangle-given-the-area-of-three-triangles%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
