Question

1. if a right triangle has legs of lengths 3 and 4, what is the length of the hypotenuse?

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

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\).

Step2: Substitute values

Let \(a = 3\) and \(b = 4\). Then \(3^{2}+4^{2}=c^{2}\), so \(9 + 16=c^{2}\), and \(c^{2}=25\).

Step3: Solve for \(c\)

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

Answer:

d. 5