Question

The altitude of a triangle is 6cm greater than its base.if its area is 108cmsquare,find its height and base​

Answer 1

let base of triangle be = x cm

then altitude = x+6 cm

area = 1/2 × b × h

108=1/2 × x × (x+6)

216=x^2 + 6x

x^2 + 6x -216 =0

x^2 + 18x - 12x - 216 = 0

x(x+18)-12(x+18) = 0

(x-12)(x+18)=0

x = 12 , -18

as length of base can't be negative then length of base be 12 cm

height = 18 cm

Answer 2

LET BASE BE X

Area = 1/2 B H= 108

=108=1/2 X*X +6

OR 108*2=X*X +6

X*X=210

X =root of 210

Base=14.49 Approximately
Height=20.49