Find the value of x in the isosceles triangle shown

x = 8√5

Step-by-step explanation:

The large triangle is divided into two smaller ones.  The right one has one leg of length 8, one leg of length x/2, and hypotenuse of length √80.

Appling the Pythagorean Theorem, we can find x:

8² + (x/2)² = (√80)²,

or:                              x^2

64 + x^2/4 = 80, or   = 80

                                    4

Then x^2 = 320 = 64*5.  Taking the square root of both sides, we get:

x = 8√5

step-by-step explanation: