Question

find the value of x in the isosceles triangle shown below. choose 1 answer.

Explanation:

Step1: Use the Pythagorean theorem

Let's consider half of the base of the isosceles triangle. The base is 4, so half - base $b = 2$, and the slant side $l=8$. According to the Pythagorean theorem $a^{2}+b^{2}=l^{2}$, where $a$ is the height (which is $x$ in our case). We can rewrite the formula for $a$ as $a=\sqrt{l^{2}-b^{2}}$.

Step2: Substitute the values

Substitute $l = 8$ and $b = 2$ into the formula $x=\sqrt{8^{2}-2^{2}}=\sqrt{64 - 4}=\sqrt{60}=2\sqrt{15}$.

Answer:

$2\sqrt{15}$