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The sum of the perimeter of 2 different squares is 40cm. The difference between the area of the 2 squares is 40cm2. Find the length of the larger square

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Answer to a math question The sum of the perimeter of 2 different squares is 40cm. The difference between the area of the 2 squares is 40cm2. Find the length of the larger square

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Maude
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Let the side length of the larger square be \(x\) cm, and the side length of the smaller square be \(y\) cm. 1. The perimeter of a square is given by \(4 \times \text{side length}\). Therefore, the sum of the perimeters of the two squares is \(4x + 4y = 40\) cm. 2. The difference between the areas of the two squares is \(x^2 - y^2 = 40\) cm². From the first equation, we can express \(y\) in terms of \(x\): \[4x + 4y = 40\] \[4y = 40 - 4x\] \[y = 10 - x\] Now, substitute this expression for \(y\) into the second equation: \[x^2 - (10 - x)^2 = 40\] \[x^2 - (100 - 20x + x^2) = 40\] \[x^2 - 100 + 20x - x^2 = 40\] \[20x - 100 = 40\] \[20x = 140\] \[x = \frac{140}{20}\] \[x = 7\] So, the side length of the larger square is 7 cm.

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