SOLUTION: Two rectangles have the same area of 480 cm^2.the diffrence between their lengths is 5cm and the diffrence between their widths is 2cm . calculate the dimension of the rectangles

Question 333343: Two rectangles have the same area of 480 cm^2.the diffrence between their lengths is 5cm and the diffrence between their widths is 2cm . calculate the dimension of the rectangles
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Two rectangles have the same area of 480 cm^2.
the difference between their lengths is 5cm and the difference between their widths is 2cm.
calculate the dimension of the rectangles
:
Let the dimension of the original rectangle be L, W
L*W = 480
L =
:
the dimensions of the other rectangle be (L-5), (w+2)
:
Areas of the two rectangles are equal
(L-5)*(W+2) = L*W
FOIL
LW + 2L - 5W - 10 = LW
:
Subtract LW from both sides
2L - 5W - 10 = 0
:
Replace L with
2() - 5W - 10 = 0
- 5W - 10 = 0
:
Multiply by W
960 - 5W^2 - 10W = 0
;
a quadratic equation
-5W^2 - 10w + 960 = 0
:
simplify, divide by -5
W^2 + 2W - 192 = 0
:
Find W using the quadratic formula

in this equation: x=w; a=1; b=2; c=-192

two solutions, but we just want the positive solution

w =
w = 12.89 cm, the width of the original rectangle
then
= 37.24 cm is the original length
Check area: 12.89*37.24 = 480.02
:
The other rectangle
12.89 + 2 = 14.89 is the width
37.24 - 5 = 32.24 is the length
check area: 14.89*32.24 = 480.05, close enough to confirm our solutions
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