Question

find the value of x in the isosceles triangle shown below.

Explanation:

Step1: Apply the Pythagorean theorem

Let's consider half - of the isosceles triangle. The base of the right - triangle formed (half of the base of the isosceles triangle) is $\frac{4}{2}=2$, and the hypotenuse is 8. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 8$ and $a = 2$, and we want to find $b$ (which is $x$). So, $x=\sqrt{8^{2}-2^{2}}$.

Step2: Calculate the value

$x=\sqrt{64 - 4}=\sqrt{60}=2\sqrt{15}$

Answer:

$2\sqrt{15}$