Question

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

Answer 1

Let the altitude of the triangle be x m.

Therefore, the base will be 3x m. 

Area of a triangle = `1/2 xx "Base" xx "Altitude"` 

∴ `1/2 xx 3x xx x = 96`   ...(∵ Area = 96 sq m) 

⇒ `x^2/2 = 32` 

⇒ x² = 64 

⇒ x = ±8 

The value of x cannot be negative.

Therefore, the altitude and base of the triangle are 8 m and (3 × 8 = 24 m), respectively.