Mixing
angles in triangles
$begingroup$
In the triangle shown, for $angle A$ to be the largest angle of the triangle, it must be that $m<x<n$. What is the least possible value of $n-m$, expressed as a common fraction? 
geometry
edited Jan 20 at 21:34
Paul Aljabar
1,175314
asked Jan 20 at 21:04
sumisumi
192
$endgroup$
add a comment |
$begingroup$
In the triangle shown, for $angle A$ to be the largest angle of the triangle, it must be that $m<x<n$. What is the least possible value of $n-m$, expressed as a common fraction?
geometry
edited Jan 20 at 21:34
Paul Aljabar
1,175314
asked Jan 20 at 21:04
sumisumi
192
$endgroup$
add a comment |
$begingroup$
In the triangle shown, for $angle A$ to be the largest angle of the triangle, it must be that $m<x<n$. What is the least possible value of $n-m$, expressed as a common fraction?
geometry
edited Jan 20 at 21:34
Paul Aljabar
1,175314
asked Jan 20 at 21:04
sumisumi
192
$endgroup$
In the triangle shown, for $angle A$ to be the largest angle of the triangle, it must be that $m<x<n$. What is the least possible value of $n-m$, expressed as a common fraction?
geometry
geometry
edited Jan 20 at 21:34
Paul Aljabar
1,175314
asked Jan 20 at 21:04
sumisumi
192
edited Jan 20 at 21:34
Paul Aljabar
1,175314
asked Jan 20 at 21:04
sumisumi
192
edited Jan 20 at 21:34
Paul Aljabar
1,175314
edited Jan 20 at 21:34
Paul Aljabar
1,175314
edited Jan 20 at 21:34
Paul Aljabar
1,175314
1,175314
asked Jan 20 at 21:04
sumisumi
192
asked Jan 20 at 21:04
sumisumi
192
asked Jan 20 at 21:04
sumisumi
192
192
add a comment |
add a comment |
1 Answer
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$begingroup$
HINT.
$x+9$ must be the largest side. But it must also be less than the sum of the other two sides, by triangular inequality.
answered Jan 20 at 21:44
AretinoAretino
24.7k21444
$endgroup$
add a comment |
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$begingroup$
HINT.
$x+9$ must be the largest side. But it must also be less than the sum of the other two sides, by triangular inequality.
answered Jan 20 at 21:44
AretinoAretino
24.7k21444
$endgroup$
add a comment |
$begingroup$
HINT.
$x+9$ must be the largest side. But it must also be less than the sum of the other two sides, by triangular inequality.
answered Jan 20 at 21:44
AretinoAretino
24.7k21444
$endgroup$
add a comment |
$begingroup$
HINT.
$x+9$ must be the largest side. But it must also be less than the sum of the other two sides, by triangular inequality.
answered Jan 20 at 21:44
AretinoAretino
24.7k21444
$endgroup$
HINT.
$x+9$ must be the largest side. But it must also be less than the sum of the other two sides, by triangular inequality.
answered Jan 20 at 21:44
AretinoAretino
24.7k21444
answered Jan 20 at 21:44
AretinoAretino
24.7k21444
answered Jan 20 at 21:44
AretinoAretino
24.7k21444
answered Jan 20 at 21:44
AretinoAretino
24.7k21444
24.7k21444
add a comment |
add a comment |
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