Read the following story problem. Sam is building a rectangular compost box. In order to fit neatly in his garden, the length needs to be three feet more than twice the width. If the perimeter is 36 feet, what is the length and width of the compost box?
Plug the values from the story problem into the formula for rectangular perimeter, which is p = 2l + 2w. The perimeter is 36, the length is 2w + 3 and the width is w. The formula reads 36 = 2(2w + 3) + 2w.
Multiply the parentheses using the distributive property: 2 x 2w is 4w and 2 x 3 = 6. Simplify the formula: 36 = 4w + 6 + 2w.
Combine the terms in the new formula that are alike. In this case, there are two terms that contain the variable w. Since both are positive, add them and simplify: 36 = 6w + 6.
Subtract 6 from both sides of the equals sign to keep the equation equivalent: 36 -- 6 = 6w + 6 -- 6. Simplify the equation: 30 = 6w.
Divide both sides of the equation by 6: 30 ÷ 6 = 6w ÷ 6 and simplify 5 = w. Therefore, the width of the compost box is 5 feet.
Plug the value for the width back into the formula to solve for length: 36 = 2l + 2(5). Simplify the expression by multiplying the parentheses: 36 = 2l + 10.
Subtract 10 from both sides of the equation: 36 -- 10 = 2l + 10 -- 10 and simplify 26 = 2l.
Divide both sides by 2: 26 ÷ 2 = 2l and simplify 13 = l. Therefore, the length of the compost box is 13 feet.