Question

the base of a triangle is 2 cm shorter than the width of a rectangle. The rectangle's length is 4 times its width and the triangle's height is the same as the rectangle's length. find the area of both figures if the difference of the two areas is 30cm2

Answer 1

from the data
rectangle:
width = x
length = 4x

triangle:
base = x-2
height = 4x

area of rectangle = x(4x) = 4x^2
area of triangle = (1/2)(x-2)(4x) = 2x^2 - 4x

given:
4x^2 - (2x^2 - 4x) = 30
2x^2 + 4x - 30 = 0
x^2 + 2x - 15=0
(x+5)(x-3) = 0
x = -5 (not possible) or x = 3

area of rect. = 4x^2 = 36
area of triangle = 2x^2 - 4x = 18-16 = 2

Answer 2

I messed up in the last line

should have said:
area of triangle = 2x^2 - 4x = 18-12 = 6