What is the value of x?

The height h of the triangle is given by Pythagoras' Theorem.
Since (4√5)²= h² + 8²
On rearranging
h² = (4√5)² - 8²
h² = (16 x 5) - 64
h² = 80 - 84 = 16
h = 4

So
x² = 4² + 24²
x² = 16 + 576 = 592
So x = +√592

Since 592 = 4² x 37
x = √(4² x 37)
= √(4²) x √37
= 4√37

y² = 80 - 64 = 16

x² = 24² + 16
x² = 592
x = 4 √37

h^2=80-64=16
x^2=16+24^2=16+576=592=16•37
x=4 sqrt(37) ~ 24.3

4√5 = √80

Pythagoras' theorum states that:
a^2 + b^2 = c^2
Where a and b are side lengths of a right angled traingle and c is the hypotenuse.

In your case, to find x we need to find the value of the dotted line. Let's call that a.

a^2 + b^2 = c^2
a^2 + 8^2 = (√80)^2
a^2 + 64 = 80
a^2 = 16
a = √16
a = 4

Now we know the value of the dotted line, so we can find x:

a^2 + b^2 = c^2
4^2 + 24^2 = x^2
16 + 576 = x^2
592 = x^2
x = √592

The question doesnt ask you to simplify so leave it as a surd.

square root of 592 or 24.331 in decimal form