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

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.