Question

1. in a right triangle with sides a = 3, b = 4, what is the length of the hypotenuse c?

a. 8
b. 6
c. 5
d. 7

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $c^{2}=a^{2}+b^{2}$, where $c$ is the hypotenuse and $a$, $b$ are the legs. Given $a = 3$ and $b = 4$, we substitute these values into the formula: $c^{2}=3^{2}+4^{2}$.

Step2: Calculate the squares

$3^{2}=9$ and $4^{2}=16$, so $c^{2}=9 + 16=25$.

Step3: Find the value of $c$

Taking the square root of both sides, $c=\sqrt{25}=5$ (we consider the positive value since length cannot be negative).

Answer:

C. 5