The perimeter of the rectangle is 5 m 6 dm and one of its sides is 6 times larger than the adjacent side.

The perimeter of the rectangle is 5 m 6 dm and one of its sides is 6 times larger than the adjacent side. Find the area of the rectangle.

A rectangle has equal opposite sides, its perimeter (the sum of all sides) is determined by the formula:

P = 2a + 2b.

Let us express the sides of such a figure, provided that P = 5 m 6 dm, and one of the sides is 6 times larger than the other, we denote the smaller side by x:

2x + 2 * 6x = 56 dm. Since 1 m = 10 dm.

2x + 12x = 56,

14x = 56. To find the second factor, divide the product by the first:

x = 56: 14 = 4 dm – the width of the rectangle, therefore the length:

6 * 4 = 24 dm.

The area is calculated by the formula:

S = a * b = 4 * 24 = 96 dm².