The hypotenuse of a grassy land in the shape of a right triangle is 1metre more than twice the shortest side. If the third side is 7metres more than the shortest side, find the sides of the grassyland.

Let the shortest side be x.
Hypotenuse = (2x + 1) m
Third side = (x + 7) m
x ² + (x + 7) ² = (2x + 1) ²
x ² + x ² + 14x + 49 = 4x ² + 4x + 1
2x ² - 10x - 48 = 0
2x ² - 16x + 6 x – 48 = 0
2x(x – 8) + 6(x – 8) = 0
(2x + 6)(x – 8) = 0
2(x + 3) = 0 or x – 8 = 0
∴ x = -3 or x = 8
The sides of the grasy land are 8, 15 and 17.
Checking:
8 ² = 64
15 ² = 225
17 ² = 289
8 ² + 15 ² = 64 + 225 = 289 = 17 ² .