Two squares have perimeters measuring 48 cm and 20 cm respectively. Determine the perimeter and the diagonal length of a new square whose area is equal to the sum of the areas of these two squares.

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15 times the square root of 2 cm13 times the square root of 2 cm16 times the square root of 2 cm17 times the square root of 2 cm12 times the square root of 2 cm

Explanation

First, calculate the side lengths of the two squares using their perimeters: side1 = 48 ÷ 4 = 12 cm, side2 = 20 ÷ 4 = 5 cm. Next, find their areas: area1 = 12² = 144 cm², area2 = 5² = 25 cm². The combined area is 144 + 25 = 169 cm². The side length of the new square equals the square root of 169, which is 13 cm. Therefore, the perimeter is 4 × 13 = 52 cm, and the diagonal is side × √2 = 13√2 cm.