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The perimeter of a rectangle is 21 inches. What is the measure of its width if its length is 3 inches greater than its width?
Let x = the width of the rectangle. Let x + 3 = the length of the rectangle, because the length is "3 more than" the width. Perimeter is the distance around the rectangle. The formula is length + width + length + width, P = l + w + l + w, or P = 2l + 2w. Substitute the let statements for l and w and the perimeter (P) equal to 21 into the formula: 21 = 2(x + 3) + 2(x). Use the distributive property on the right side of the equation: 21 = 2x + 6 + 2x. Combine like terms of the right side of the equation: 21 = 4x + 6. Subtract 6 from both sides of the equation: 21 - 6 = 4x + 6 - 6. Simplify: 15 = 4x. Divide both sides of the equation by 4: 15/4 = 4x/4. The variable is now alone: 3.75 = x.
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