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Price Match

Age 7 to 11 Challenge Level:
You might like to try Through the Window before this challenge.

​In a particular shop, the price of windows is calculated according to the area of glass used and the length of frame needed.

In the picture below, glass costs £10 for an area of one small square, plus £5 for every square edge of frame.

 




If we call the area of the glass A and the perimeter of the window P, how would you express the cost of the window in terms of A and P?

Use your formula to find pairs of rectangular windows that are different sizes but cost the same.