Answer:
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
