Posted by Anonymous on .
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

calculus 
Anonymous,
from the data
rectangle:
width = x
length = 4x
triangle:
base = x2
height = 4x
area of rectangle = x(4x) = 4x^2
area of triangle = (1/2)(x2)(4x) = 2x^2  4x
given:
4x^2  (2x^2  4x) = 30
2x^2 + 4x  30 = 0
x^2 + 2x  15=0
(x+5)(x3) = 0
x = 5 (not possible) or x = 3
area of rect. = 4x^2 = 36
area of triangle = 2x^2  4x = 1816 = 2 
Oops  calculus 
Reiny,
I messed up in the last line
should have said:
area of triangle = 2x^2  4x = 1812 = 6