SOLUTION: The perimeter of a rectangle is 28cm. If the length were decreased by 2cm and the width increased by 2cm, the area would be increased by 8cm. Find the length and width of the rect

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Question 460464: The perimeter of a rectangle is 28cm. If the length were decreased by 2cm and the width increased by 2cm, the area would be increased by 8cm.
Find the length and width of the rectangle.
Answer by Tatiana_Stebko(1539) About Me  (Show Source):
You can put this solution on YOUR website!
Let x is the length of a rectangle
Let y is the width of a rectangle
The perimeter of a rectangle is 2x%2B2ycm, than 2x%2B2y=28
The area of the rectangle is xycm%5E2
If the length were decreased by 2cm, so the length would be %28x-2%29cm and the width increased by 2cm, so the width would be %28y%2B2%29cm, the area is %28x-2%29%28y%2B2%29cm%5E2 and the area would be increased by 8cm, so xy%2B8=%28x-2%29%28y%2B2%29.
System of equations
system%282x%2B2y=28%2Cxy%2B8=%28x-2%29%28y%2B2%29%29
system%28x%2By=14%2Cxy%2B8=xy%2B2x-2y-4%29
system%28x%2By=14%2C2x-2y=12%29
system%28y=14-x%2Cx-y=6%29
system%28y=14-x%2Cx-%2814-x%29=6%29
system%28y=14-x%2C2x=20%29
system%28x=10%2Cy=14-10%29
system%28x=10%2Cy=4%29
x=10cm is the length of a rectangle
y=4cm is the width of a rectangle
.
Check
system%282%2A10%2B2%2A4=28%2C10%2A4%2B8=%2810-2%29%284%2B2%29%29
system%2828=28%2C48=48%29-correct
.
Answer: x=10cm is the length of a rectangle, y=4cm is the width of a rectangle