SOLUTION: The ratio of the perimeter of rectangle P to the perimeter of rectangle Q is 2:5. The area of rectangle P is 12 square feet. What is the area of rectangle Q?
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Question 847137: The ratio of the perimeter of rectangle P to the perimeter of rectangle Q is 2:5. The area of rectangle P is 12 square feet. What is the area of rectangle Q?
You can put this solution on YOUR website! x and y is width and length of rectangle P.
xy=A for rectangle P
2x+2y=p for rectangle P, using lowercase p for perimeter.
"area of rect P is 12 ft^2";
A=xy=12.
You could find y as a formula and substitute into the perimeter equation for rectangle P.
y=12/x;
2x+2(12/x)=p
2x+24/x=p
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While being unproductive here, one should know that if the perimeters of P and Q are in a certain ratio, then the side lengths are also in this ratio. If the two rectangles are similar, then the problem could be easier.
Rectangle P.
x and y as before.
2x+2y=p and xy=A, for P.
2/5 is Perimeter P to perimeter Q.
Rectangle Q.
2(5/2)x+2(5/2)y=perimQ
2(5/2)(x+y)=perimQ
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(5/2)x(5/2)y=areaQ
Recall that .
Substituting this value for xy, the area of P, into the "areaQ" equation, we can compute the area of rectangle Q.
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