Final answer:
To find the length of each side of a rectangle, given its perimeter and diagonal length, we can use the Pythagorean theorem. We can solve these equations simultaneously to find the length and width of the rectangle. Therefore, the length of each side of the rectangle is 12.3 m.
Step-by-step explanation:
To find the length of each side of a rectangle, given its perimeter and diagonal length, we can use the Pythagorean theorem. Let's assume the length of the rectangle is L and the width is W. The perimeter is given by the formula: Perimeter = 2L + 2W. In this case, the perimeter is 53.2 m, so we can write the equation as: 2L + 2W = 53.2. The diagonal length can be found using Pythagorean theorem: Diagonal^2 = L^2 + W^2. In this case, the diagonal length is 19 m, so we can write the equation as: 19^2 = L^2 + W^2.
We can solve these equations simultaneously to find the length and width of the rectangle.
1. From 2L + 2W = 53.2, we can simplify it to L + W = 26.6.
2. From 19^2 = L^2 + W^2, we can substitute W = 26.6 - L into the equation: 19^2 = L^2 + (26.6 - L)^2.
3. Expand the equation and simplify it to: 2L^2 - 53.2L + 212.24 = 0.
4. Solve the quadratic equation and find the value of L.
5. Substitute the value of L into L + W = 26.6 to find the value of W.
Therefore, the length of each side of the rectangle is 12.3 m.