Question

A field is in the shape of a right-angled triangle. Its hypotenuse is 1 m larger than twice the smallest side. If its third side is 7 m larger than the smallest side, then find sides of the field.

Answer 1

Let length of smallest side = x m

hypotenuse = (2x + 1) m and third side = (x + 7) m

By pythagorus theorem,

(hypotenuse)² = sum of square of other both

⇒ (2x + 1)² = x² + (x + 7)²

⇒ 4x² + 4x + 1 = 2x² + 14x + 49

⇒ 2x² – 10x – 48 = 0

⇒ x² – 5x – 24 = 0

⇒ x² – 8x + 3x – 24 = 0

⇒ x(x – 8) + 3(x – 8) = 0

⇒ (x – 8) (x + 3) =0

⇒ x = 8, – 3

⇒ x = 8 [∵ x = -3 not possible]

hypotenuse = 2 × 8 + 1 = 17 m

and third side = 8 + 7 = 15 m.

Hence, the length of sides of the field is 8 m, 17 m, and 15 m.