Please help find the value of x for this equation

A

Step-by-step explanation:

We would like to find the value of x.

Since the triangle is isosceles, the drawn altitude bisects the base of length 8. This means that the big triangle is split into two congruent triangles with base 4 and height 5.

Notice that by definition, as well, the altitude of 5 is perpendicular to the base of length 8. So, we have two right triangles, each with legs of 4 and 5 and hypotenuse x.

We apply the Pythagorean Theorem, which states that for a right triangle with legs a and b and hypotenuse c:

a² + b² = c²

Here, we have:

4² + 5² = x²

16 + 25 = x²

41 = x²

x = √41

The answer is thus A.

~ an aesthetics lover