Henry knows that the area of a rectangle is 30 square inches. The perimeter is 22 inches. If the length is 1 inch longer than the width, what are the length and width of Henry’s rectangle? Explain how you know.

2(w + w+1) = 22

so w = 5
sure enough, the length is 5+1 = 6
and the area is 30

Did you know?

Did you know that the length and width of a rectangle can be determined even if only the area and perimeter are known? In this case, Henry's rectangle has an area of 30 square inches and a perimeter of 22 inches. By using algebra, we can solve this problem by setting up equations. Let's assume the width of the rectangle is "w" inches. Since the length is 1 inch longer than the width, we can say the length is "w + 1" inches. The formula for the area of a rectangle is length multiplied by width, so we can set up the equation (w + 1) * w = 30. Similarly, the formula for the perimeter is twice the length plus twice the width, giving us 2(w + 1) + 2w = 22. By solving these equations simultaneously, we can find that the width is 5 inches and the length is 6 inches.