Question

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

Answer 1

Let the shortest side = x
Hypotenuse = 2x + 1
and third side = x + 7
According to the condition,
(2x + 1)² = x² + (x + 7)2
⇒ 4x² + 4x + 1 = x² + x² + 14x + 49
⇒ 4x² + 4x + 1 - 2x² - 14x - 49 = 0
⇒ 2x² - 10x - 48 = 0
⇒ x² - 5x - 24 = 0  ...(Dividing by 2)
⇒ x² - 8x + 3x - 24 = 0
⇒ x(x - 8) + 3(x - 8) = 0
⇒ (x - 8)(x + 3) = 0
EIther x - 8 = 0,
then x = 8
or
x + 3 = 0,
then x = -3,
but it is not possible as it is negative.
∴ Shortest side = 8m
Third side
= x + 7
= 8 + 7
= 15m
and hypotenuse
= 2x + 1
= 8 x 2 + 1
= 16 + 1
= 17m.