Question

a triangle is a right triangle if the lengths, a, b, and c, of its three sides satisfy the following equation: $a^{2}+b^{2}=c^{2}$. which of the following is a right triangle? a. a triangle with sides measuring 13, 15, and 19 b. a triangle with sides measuring 17, 25, and 36 c. a triangle with sides measuring 20, 21, and 29 d. a triangle with sides measuring 18, 23, and 41

Explanation:

Step1: Recall Pythagorean theorem

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

Step2: Check option A

$a = 13$, $b = 15$, $c = 19$. Calculate $a^{2}+b^{2}=13^{2}+15^{2}=169 + 225=394$ and $c^{2}=19^{2}=361$. Since $394
eq361$, it's not a right - triangle.

Step3: Check option B

$a = 17$, $b = 25$, $c = 36$. Calculate $a^{2}+b^{2}=17^{2}+25^{2}=289+625 = 914$ and $c^{2}=36^{2}=1296$. Since $914
eq1296$, it's not a right - triangle.

Step4: Check option C

$a = 20$, $b = 21$, $c = 29$. Calculate $a^{2}+b^{2}=20^{2}+21^{2}=400 + 441=841$ and $c^{2}=29^{2}=841$. Since $a^{2}+b^{2}=c^{2}$, it is a right - triangle.

Step5: Check option D

$a = 18$, $b = 23$, $c = 41$. Calculate $a^{2}+b^{2}=18^{2}+23^{2}=324+529 = 853$ and $c^{2}=41^{2}=1681$. Since $853
eq1681$, it's not a right - triangle.

Answer:

C. a triangle with sides measuring 20, 21, and 29