The perimeter of the rectangle is 162 in and one of the sides is 47 in. Find the area of the rectangle.

It is known that the perimeter of a rectangle (P) is equal to the sum of the lengths of all its sides:

P = a + b + a + b = 2a + 2b, where a is the length of the rectangle, b is the width of the rectangle.

It turns out that, knowing the perimeter of the rectangle and one of its sides, you can find the other side by the formula:

b = (P – 2a): 2.

Find the second side of the given rectangle:

b = (162 – 2 * 47): 2,

b = (162 – 94): 2,

b = 68: 2,

b = 34.

This means that the length of the second side of the rectangle is 34 dm.

Knowing the sides of the rectangle, you can calculate its area (S) by the formula: S = a * b.

Let’s calculate the area of ​​a given rectangle: S = 47 * 34 = 1598 dm2.

Answer: 1598 dm2.