Answer:
504 cm^2.
Explanation:
By Pythagoras:
(2x + 5)^2 = (2x + 3)^2 + (x - 14)^2
4x^2 + 20x + 25 = 4x^2 + 12x + 9 + x^2 - 28x + 196
20x - 12x + 28x + 25 - 9 - 196 = x^2
x^2 - 36x + 180 = 0
(x - 6)(x - 30) = 0
x = 6, 30.
As one of the sides is x - 14, x mst be 30 as its length has to be positive.
So the area of the triangle
= 1/2 * (x - 14) 8 (2x + 3)
= 1/2 * (30-14)(60 + 3)
= 1/2 * 16 * 63
= 504 cm^2.