Question

if one leg of a right triangle is 5 units and the hypotenuse is 13 units, what is the length of the other leg? a. 15 units b. 10 units c. 8 units d. 12 units

Explanation:

Step1: Apply Pythagorean theorem

$$a^{2}+b^{2}=c^{2}$$
Let \(a = 5\), \(c = 13\), and \(b\) be the unknown leg.

Step2: Substitute values

$$5^{2}+b^{2}=13^{2}$$
$$25 + b^{2}=169$$

Step3: Solve for \(b^{2}\)

$$b^{2}=169 - 25$$
$$b^{2}=144$$

Step4: Find \(b\)

$$b=\sqrt{144}$$
$$b = 12$$

Answer:

D. 12 units