Question

question 3
10 pts
g.gsr.6.3 (mc)
find the value of x.
image of a right triangle with one leg 12, hypotenuse 20, and the other leg x
options:
x = 18
x = 17
x = 16
x = 15

Explanation:

Step1: Identify the triangle type

This is a right - triangle, so we can use the Pythagorean theorem. The Pythagorean theorem states that for a right - triangle with legs \(a\), \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Here, one leg \(a = 12\), the hypotenuse \(c = 20\), and the other leg is \(x\). So we can rewrite the formula as \(x^{2}+12^{2}=20^{2}\).

Step2: Solve for \(x^{2}\)

First, calculate \(12^{2}=144\) and \(20^{2}=400\). Then, from \(x^{2}+144 = 400\), we can get \(x^{2}=400 - 144\).

Step3: Calculate \(x^{2}\) and \(x\)

\(400-144 = 256\), so \(x^{2}=256\). Taking the square root of both sides, since \(x\) represents the length of a side of a triangle (and length is non - negative), we have \(x=\sqrt{256}=16\).

Answer:

\(x = 16\) (corresponding to the option "x = 16")