Question

In a right-angled triangle, altitude is 2 cm longer than its base. Find the dimensions of the right-angled triangle given that the length of its hypotenuse is 10 cm.

Answer 1

Let x cm be the base of the right-angled triangle.

As a result, the altitudeude = (x + 2) cm.

Also, hypotenuse = 10 cm

We have the Pythagorean theorem.

(Base)² + (Altitude)² = (Hypotenuse)²

⇒ x² + (x + 2)² = 10²

⇒ x² + x² + 4x + 4 = 100

⇒ 2x² + 4x – 96 = 0

⇒ 2x + 2x – 48 = 0

⇒ x² + (8 – 6)x – 48 = 0

⇒ x² + 8x – 6x – 48 = 0

⇒ x(x + 8) – 6(x + 8) = 0

⇒ (x – 6)(x + 8) = 0

⇒ (x + 8) = 0 or (x – 6) = 0

⇒ x = – 8 or x = 6

A triangle's sides cannot be negative.

So, x = 6.

As a result, the right-angled triangle's base is 6 cm and its altitude is 6 + 2 = 8 cm.

As a result, the right-angled triangle's dimensions are 8 cm, 6 cm, and 10 cm.