Question

The area of a right-angled triangle is 165 sq meters. Determine its base and altitude if the latter exceeds the former by 7 meters.

Answer 1

Let the base be x m.

Therefore, the altitude will be (x + 7) m.

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

∴ `1/2 xx x xx (x + 7) = 165` 

⇒ x² + 7x = 330 

⇒ x² + 7x – 330 = 0 

⇒ x² + (22 – 15)x – 330 = 0 

⇒ x² + 22x – 15x – 330 = 0 

⇒ x(x + 22) – 15(x + 22) = 0 

⇒ (x + 22) (x – 15) = 0 

⇒ x = –22 or x = 15 

The value of x cannot be negative. 

Therefore, the base is 15 m and the altitude is {(15 + 7) = 22 m}.