Question

determine whether a triangle with the given side lengths is a right triangle.

side lengths	right triangle	not a right triangle	not enough information
(b) 7, 24, 25
(c) 5, 7, 9
(d) 11, 24, 26

Explanation:

Step1: Recall Pythagorean theorem

$a^{2}+b^{2}=c^{2}$, where $c$ is the longest side.

Step2: Check (a) 22, 25, 22

$22^{2}+22^{2}=484 + 484=968$, $25^{2}=625$, not a right - triangle.

Step3: Check (b) 7, 24, 25

$7^{2}+24^{2}=49+576 = 625$, $25^{2}=625$, right - triangle.

Step4: Check (c) 5, 7, 9

$5^{2}+7^{2}=25 + 49=74$, $9^{2}=81$, not a right - triangle.

Step5: Check (d) 11, 24, 26

$11^{2}+24^{2}=121+576 = 697$, $26^{2}=676$, not a right - triangle.

Answer:

(a) Not a right triangle
(b) Right triangle
(c) Not a right triangle
(d) Not a right triangle