The length of a rectangle is 4 less than 3 times the width. perimeter is 40 inches. what is the area of the rectangle?

Area = 84 in²

Step-by-step explanation:

In order to find the area of the rectangle, you need to first set up an equation to find the length based on the information already given in the problem.  Since the perimeter = 40 and the formula to find perimeter of a rectangle is:       P = 2W + 2L, where W = width and L=Length, we can solve for 'L' by putting in the values given:

P = 2W + 2L  or  40 = 2W + 2(3W - 4)

The length of the rectangle is '4 less than 3 times the width'.  This can be written as the expression '3W - 4'.

Distribute:  40 = 2W + 2(3W - 4)  or 40 = 2W + 6W - 8

Combine like terms:  40 = 8W - 8

Add '8' to both sides:  40 + 8 = 8W - 8 + 8 or 48 = 8W

Divide both sides by '8':  48/8 = 8W/8 or 6 = W

Solve for L:  3W - 4 or 3(6) - 4 = 18 - 4 = 14

Since L=14 and W = 6, we can solve for Area using the formula: A = LxW or A = (14)(16) = 84in².

associative property of multiplication