SOLUTION: A rectangle is 4 times as long as it is wide. A second rectangle is 5 centimenters longer and 2 centimeters wider than the first. The area of the second rectangle is 270 square c

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Question 39302: A rectangle is 4 times as long as it is wide. A second rectangle is 5 centimenters longer and 2 centimeters wider than the first. The area of the second rectangle is 270 square centimeters greater than the first. What are the dimensions of the original rectangle?
Found 2 solutions by Nate, Paul:
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
Original:
length = 4w
width = w
Second rectangle:
length: 5 + 4w
width = 2 + w
Equations:
First triangle: a+%2B+270+=+a
%284w%29%28w%29+%2B+270+=+%285%2B4w%29%282%2Bw%29
4w%5E2+%2B+270+=+4w%5E2+%2B+13w+%2B+10
260+=+13w
20+=+w
80+=+l
Second triangle:
w+=+22
l+=+85

Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
First rectangle is 4x, and its width is x
Second rectangle is 4x+5 in length and x+2 in width
Area of first is 4x*x=4x%5E2
Area of second = 4x%5E2%2B270
EQUATION:
4x%5E2%2B270=%284x%2B5%29%28x%2B2%29
4x%5E2%2B270=4x%5E2%2B13x%2B10
13x=260
x=20
4(20)=80
Hence, the dimensions of the original rectangle are 80cm * 20cm.
Paul.