Posted by **Anonymous** on Wednesday, September 8, 2010 at 10:46pm.

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**, Thursday, September 9, 2010 at 1:10am
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

- Oops - calculus -
**Reiny**, Thursday, September 9, 2010 at 1:13am
I messed up in the last line

should have said:

area of triangle = 2x^2 - 4x = 18-12 = 6

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