Question

The area of a triangle is 30 cm². Find the base if the altitude exceeds the base by 7 cm.

Answer 1

Let base QR = x cm

altitude (PS) = (x + 7) cm

Now, area of ΔPQR = \(\frac { 1 }{ 2 }\) x base x altitude

30 = \(\frac { 1 }{ 2 }\) x QR x PS

= \(\frac { 1 }{ 2 }\) × x × (x + 7)

⇒ 60 = x² + 7x

⇒ x² + 7x – 60 = 0

⇒ x² + 12x – 5x – 60 = 0

⇒ x (x + 12) – 5 (x + 12) = 0

⇒ (x + 12)(x – 5) = 0

⇒ x = 5 or x = -12

⇒ x = -12 is not admissible

⇒ x = 5 cm

base (x) = 5 cm

and corresponding altitude 

= x + 7 = 5 + 7 

= 12 cm.