Question

The base of a triangle is 4 cm longer than its altitude.Area is 48sq.cm Find base and altitude

Answer 1

Let altitude be x cm
base = x+4 cm

Area = (1/2)×base×altitude
⇒48= (1/2)×x×(4+x)
⇒x² +4x - 96 = 0
⇒x² +12x - 8x - 96 = 0
⇒x(x+12) -8(x +12) =0
⇒(x+12)(x-8) = 0
so, x+12 = 0 or x-8 = 0
⇒x = -12 or 8

x can't be negative , so x = 8
Altitude = 8 cm 
Base = 12 cm

Answer 2

Answer:

Step-by-step explanation:

Given :-

Area of Triangle = 48 cm²

To Find :-

Base and Altitude

Formula to be used :-

Area = (1/2) × base × altitude

Solution :-

Let altitude be x cm

And the base be x + 4 cm

Area = (1/2) × base × altitude

⇒ 48 = (1/2) × x × (4 + x)

⇒ x² + 4x - 96 = 0

⇒ x² + 12x - 8x - 96 = 0

⇒ x(x + 12) - 8(x + 12) =0

⇒ (x + 12) (x - 8) = 0

x + 12 = 0 or x - 8 = 0

⇒ x = - 12 (neglected) or 8

Altitude = 8 cm 

Base = 8 + 4 =  12 cm

Hence, Base and Altitude of triangle are 12 cm and 8 cm.