Question

An altitude of a triangle is five thirds the length of
its corresponding base. If the altitude be increased
by 4 cm and the base decreased by 2 cm, the area
of the triangle remains the same. Find the base
and the altitude of the triangle.​

Answer 1

Let the base of the traingle be x cm

Its corresponding altitude = 5x/3 cm

Area = 1/2 × base × altitude

A = 1/2 × x × 5x/3 – ( 1 )

Now if altitude be increased by 4 cm and the base decreased by 2 cm

new altitude = ( 5x/3 + 4 ) cm

new base = ( x – 2 ) cm

A = 1/2 (x– 2) ( 5x/3 + 4 ) – ( 2 )

equating ( 1 ) and ( 2 )

1/2 (x– 2) ( 5x/3 + 4 ) = 1/2 × x × 5x/3

( x – 2 ) ( 5x + 12 ) / 3 = 5x² / 3

5x² + 12x – 10x – 24 = 5x²

2x – 24 = 0

2x = 24

x = 24/2

x = 12 cm

Ans : Base of the triangle is 12 cm Altitude of the triangle is 60/3 cm