Question

The altitude of a triangle is 2/3 of the length of the corresponding base. If the altitude is decreased by 1cm and base is increased by 4cm, the area of the new triangle remains the same. Find the base and altitude of the original triangle.

Answer 1

let the base be b cm
height =2/3b
area1 =1/2*2/3b*b
=1/3b^2
new height=2/3b-1
base= b+4
area2= 1/2*(2/3b-1)*(b+4)
1/2(2/3b^2+5/3b-4)
since area1=area2
1/3b^2=1/3b^2+5/6b-2
solving we get b =12/5
height=2/3*12/5
=8/5