Question

The base of a triangle is 6 cm shorter than the altitude to that base. How do you find the length of the base and the altitude if the are of the triangle is 56 cm^2?

Answer 1

let the altitude be x cm

therefore base is x-6 cm

area of triangle = 1/2 ×base × altitude

56= 1/2×(x-6)×x

112=x^2-6x

so

x^2-6x-112=0

by middle term split method

x^2-14x+8x-112=0

x(x-14)+8(x-14)=0

(x+8)(x-14)=0

x=-8 (not possible)

x=14

therefore length of altitude is 14cm

and base is x-6= 14-6=8 cm