Question

A square a rectangle have the same perimeter of a square has a side length of 8x units. The rectangle has a length of (5x + 12) and a width of 10 units. what will be the perimeter of both a rectangle and the square

Answer 1

Explanation:

The perimeter of a square is calculated by multiplying the length of one side by 4. Since the side length of the square is 8x units, the perimeter of the square is 4 * 8x = 32x units.

The perimeter of a rectangle is calculated by adding the lengths of all four sides or by using the formula 2 * (length + width). Since the length of the rectangle is (5x + 12) units and the width is 10 units, the perimeter of the rectangle is 2 * ((5x + 12) + 10) = 10x + 44 units.

Since both shapes have the same perimeter, we can set their perimeters equal to each other and solve for x:

32x = 10x + 44 22x = 44 x = 2

Substituting this value of x back into the expression for the perimeter of either shape, we find that the perimeter of both the square and the rectangle is 64 units.