Answer:
x = 6
Explanation:
the diagonal AC divides the rectangle into 2 right triangles.
Consider the right triangle ABC with legs AB , BC and hypotenuse AC
using Pythagoras' identity in right triangle ABC
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
AB² + BC² = AC² ( substitute values )
x² + (x + 2)² = (x + 4)² ← expand factors using FOIL
x² + x² + 4x + 4 = x² + 8x + 16
2x² + 4x + 4 = x² + 8x + 16 ( subtract x² + 8x + 16 from both sides )
x² - 4x - 12 = 0 ← in standard form
(x - 6)(x + 2) = 0 ← in factored form
equate each factor to zero and solve for x
x - 6 = 0 ⇒ x = 6
x + 2 = 0 ⇒ x = - 2
however , x > 0 , then x = 6