Answer:
x = 5
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
x² + (x + 7)² = 13² ← expand and simplify left side
x² + x² + 14x + 49 = 169 ( subtract 169 from both sides )
2x² + 14x - 120 = 0 ( divide through by 2 )
x² + 7x - 60 = 0 ← in standard form
(x + 12)(x - 5) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 12 = 0 ⇒ x = - 12
x - 5 = 0 ⇒ x = 5
But x > 0 , thus x = 5
