Chapter 8, Problem 11CT

To determine

To find: Whether the triangle formed with sides having lengths $7,7,10$ named is acute, right, or obtuse.

Answer to Problem 11CT

The triangle is obtuse.

Explanation of Solution

Given information:

Length of the sides are $7,7,10$ .

Since $7+7=14>10$

Thus, the sum of two sides greater than the third side.

Therefore, the triangle formed with given lengths.

And also we know that if $a,b,c$ are lengths of three sides of a triangle then

$i.$ The triangle is said to be right angle triangle, if $a^2+b^2=c^2$

$ii.$ The triangle is said to be obtuse triangle, if $a^2+b^2<c^2$

$iii.$ The triangle is said to be acute triangle, if $a^2+b^2>c^2$

From given lengths, we observe that $7^2+7^2=49+49$

$=98<100={10}^2$

$\therefore 7^2+7^2<{10}^2$

Hence, the triangle is obtuse.