Question

The base of a triangle is 8 cm greater than the height. The area is 24cm^2. What is the base and height?

Answer 1

Let height is x.
So base=x+8
area of triangle=1/2*b*h
given area=24
so 24=1/2*b*h
2*24=(x+8)*x
48=(x^2+8x)
x^2+8x-48=0
x^2+(12x-4x)-48=0
x^2+12x-4x-48=0
x(x+12)-4(x+12)=0
(x+12)(x-4)=0
x=4,-12
so taking x=4
height=4cm
base=x+8=4+8=12cm

Answer 2

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