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

## Answer this Question

## Related Questions

- geometry - a rectangle and an equilateral triangle have the same perimeter the ...
- math - A right rectangle and a right triangle prism have the same height. If ...
- math - a right rectangle and a right triangle prism have the same height. If the...
- basic geometric - 10. a rectangle has width the same as a side of a square whose...
- algebra - sooo confusing... 6. (¼ + 7/8)(9/13) A81/13 B17/104 C81/104 D17/29 E17...
- algebra , help - Can someone help me set up the equations thanks. Directions: ...
- Algebra Homework, HELP! - 1) A rectangle has an area of 297 square inches and a...
- geometry - The perimeter of the rectangle is 19 inches. The perimeter of the ...
- basic geometry - A rectangle has width the same asa a side of a square whose ...
- algebra 1 - Evan is making a table that will be created in the shape of the ...