Answer:
x = 8
Step-by-step explanation:
Since the triangle is isosceles then the segment from the vertex is a perpendicular bisector, dividing the triangle into 2 right triangles.
Using Pythagoras' identity on the right triangle on the left
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
([tex]\frac{1}{2}[/tex] x )² + 8² = ([tex]\sqrt{80}[/tex])²
[tex]\frac{1}{4}[/tex] x² + 64 = 80 ( subtract 64 from both sides )
[tex]\frac{1}{4}[/tex] x² = 16 ( multiply both sides by 4 )
x² = 64 ( take the square root of both sides )
x = [tex]\sqrt{64}[/tex] = 8 ← positive value only required
