the length of a rectangle is 5 less than twice the width. if the perimeter of the rectangle is 146, find the area of the rectangle.

The area of the rectangle is 1222 units²

Step-by-step explanation:

The formula of the perimeter of a rectangle is P = 2 (L + W), where L is its length and W is its width

The formula of the area of a rectangle is A = L * W

∵ The length of a rectangle is 5 less than twice the width

- Assume that the width of the rectangle is x units and multiply

x by 2 and subtract 5 from the product to find its length

∴ W = x

∴ L = 2x - 5

- Use the formula of the perimeter above to find its perimeter

∵ P = 2 (2x - 5 + x)

∴ P = 2 (3x - 5)

- Multiply the bracket by 2

∴ P = 6x - 10

∵ The perimeter of the rectangle is 146 units

∴ P = 146

- Equate the two expression of P

∴ 6x - 10 = 146

- Add 10 to both sides

∴ 6x = 156

- Divide both sides by 6

∴ x = 26

Substitute the value of x in W and L expressions

∴ W = 26 units

∴ L = 2 (26) - 5 = 52 - 5

∴ L = 47 units

Now use the formula of the area to find the area of the rectangle

∵ A = 47 * 26

∴ A = 1222 units²

∴ The area of the rectangle is 1222 units²