Question

The hypthenuse of a right triangle is 1m less than twice the shortest side. If the third side is 1m more than the shortest side,find the sides of the triangle.

Answer 1

Let the shortest side of the right triangle be x m

Then,

Hypotenuse = (2x - 1) m

And Third side = (x + 1) m

Using Pythagoras Theorem

Hypotenuse² = (Side 1)² + (Side2)²

(2x - 1)² = x² + (x + 1)²

4x² - 4x + 1 = x² + x² + 2x + 1

4x² - 4x + 1 = 2x² + 2x + 1

⇒ 4x² - 2x² - 4x - 2x + 1 - 1 = 0

⇒ 2x² - 6x = 0

⇒ 2x (x - 3) = 0

⇒ 2x = 0 or x - 3 = 0

⇒ x = 0 or x = 3

⇒ x = 3

[ By rejecting x = 0 Since , Side cannot be 0 ]

Thus, x = 3

⇒ 2x - 1 = 2(3) - 1 = 5 { Hypotenuse }

⇒ x + 1 = 3 + 1 = 4 { Third side }

Hence ,

The sides of given right angled triangle are 3m , 4m and 5m