The area of a right-angled triangle is 96 m². If its base is three times its altitude, find the base.
Quadratic Equations
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Question

The area of a right-angled triangle is 96 m2. If its base is three times its altitude, find the base.

KnowledgeBoat · Accepted Answer

Let length of altitude be x meters.

Given,

Area of right triangle = 96 m²

Base of triangle is 3 times altitude.

Length of base = 3x meters

By formula,

⇒ Area of triangle = $\dfrac{1}{2}$ × base × altitude

⇒ 96 = $\dfrac{1}{2}$ × 3x × x

⇒ 96 × 2 = 3x²

⇒ 192 = 3x²

⇒ x² = $\dfrac{192}{3}$

⇒ x² = 64

⇒ x = $\sqrt{64}$

⇒ x = 8 meters.

Length of altitude of triangle = 8 m

Length of base of triangle = 3 × 8 = 24 m.

Hence, length of base = 24 m.

Mathematics