Question

9 of 30
what is the side length of a right triangle with hypotenuse 26 and one side 10?
a 23
b 22
c 24
d 25

Explanation:

Step1: Apply Pythagorean theorem

Let the hypotenuse be $c = 26$, one - side be $a = 10$, and the other side be $b$. The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, so $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

Substitute $c = 26$ and $a = 10$ into the formula: $b=\sqrt{26^{2}-10^{2}}=\sqrt{(26 + 10)(26 - 10)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). Then $b=\sqrt{36\times16}=\sqrt{576}$.

Step3: Calculate the square - root

$\sqrt{576}=24$.

Answer:

C. 24