Question

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

Explanation:

Step1: Divide isosceles triangle

Draw the altitude from the vertex angle to the base of the isosceles triangle. It bisects the base. The base is $4$, so half - base is $2$.

Step2: Apply Pythagorean theorem

In the right - triangle formed, the hypotenuse is $8$ and one leg is $2$. Let the other leg be $x$. By the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 8$ and $a = 2$. Then $x=\sqrt{8^{2}-2^{2}}=\sqrt{64 - 4}=\sqrt{60}=2\sqrt{15}$ (wrong, re - analyze).

Step3: Correctly identify right - triangle

The right - triangle has hypotenuse $8$ and one leg $4$. Let the other leg be $x$.

Step4: Use Pythagorean theorem again

By the Pythagorean theorem $x=\sqrt{8^{2}-4^{2}}=\sqrt{64 - 16}=\sqrt{48}=4\sqrt{3}$.

Answer:

$x = 4\sqrt{3}$