5. The length of a rectangle is 3 inches less than its width. If the perimeter is 74 inches, find the dimensions of the rectangle.

length is 17 in, width is 20

Step-by-step explanation:

let's shape this as an algebraic equation, where x= the length of one side.

since the width is 3 inches longer than the length, x will be the length and x+3 will be the width.

the perimeter is 74 in, and the perimeter is the added length of all sides. in a rectangle, 2 sides are the length and 2 sides are the width, so:

74 = 2x + 2(x + 3)

let's distribute the 2.

74 = 2x + 2x + 6

now, we combine the x's.

74 = 4x + 6

after this step, subtract 6 from the right to add it to the left side.

68 = 4x

finally, divide both sides by 4.

17 = x

perfect! now that we know the length, we just have to add 3 to find the width.

17 + 3 = 20