Question

Triangle altitude is five third of its base . If the altitude increased by 4 and base decreased by 2 the the area will be same . What is the length of base and altitude

Answer 1

Hi !

Let the base = b = x
Altitude = h = 5/3 x
Original area = 1/2bh
                      = 1/2*x * 5/3x
                      = 5x²/6

new altitude = h' = 5x/3 + 4 = (5x+12)/3
new base = b' = x- 2

new area = 1/2*(x-2) (5x+12/3)

As the area in both cases is same,

1/2*(x-2) (5x+12/3) = 5x²/6
1/6*(5x² - 10x + 12x - 24) = 5x²/6

6 get cancelled on both sides,

5x² + 2x - 24 = 5x²

2x - 24 = 0

2x = 24

x = 24/2

x = 12

base = x = 12 cm

altitude = h = 5/3x = 5/3*12 = 20 cm

Hence,base is 12 cm and altitude is 20cm