Answer:
x = 15
Step-by-step explanation:
Consider the right triangle on the left with hypotenuse h₁ , then
Using Pythagoras' identity
h₁² = x² + 9²
Consider the right triangle on the right with hypotenuse h₂ , then
h₂² = x² + 25²
Now consider the large right triangle with legs h₁ and h₂ , then
h₁² + h₂² = (9 + 25)² , substitute values
x² + 9² + x² + 25² = 34² , that is
2x² + 81 + 625 = 1156
2x² + 706 = 1156 ( subtract 706 from both sides )
2x² = 450 ( divide both sides by 2 )
x² = 225 ( take the square root of both sides )
x = [tex]\sqrt{225}[/tex] = 15
