Question

The altitude of a triangle is two third the length of its corresponding base. If the altitude 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

ANSWER:-

Let the base=x cm

altitude=2/3xcm

area of triangle = 1/2×base×height

=1/2×x×2/3x

=1/2×2/3x2cm2(1)

area=1/2(x-2)(2x+12/3)_(2)

1÷2×2÷3x2=1÷2(x-2)(2x+12÷3)

2x2=1÷2(x-2)(2x+12÷3)×2×3

2x2=(x-2)(2x+12)

2x2=2x2+12x-4x-24

2x2=2x2+8x-24

2x2-2x2-8x=-24

-8x=-24

x=24÷8

=3

so,base=3cm

and,altitude=2/3x

=2/3×3

=2cm.