Question

The perimeter of a rectangle is 30 inches. The width of the rectangle is two-thirds of its

length, as shown.



What are the length and the width of the rectangle? Check your solution.

Answer 1

The length is
`9` inches and the width is
`30` inches.

Explanation:

The perimeter of the rectangle is
`2x + (4x)/(3) = 30`. We multiply
`3` by both sides which will give us
`6x + 4x = 90`. Adding, we have
`10x = 90`. Dividing
`10` by both sides will give us
`x = 9`. The length of the rectangle is
`9`, and the width is
`\frac23 \cdot 9 = 6.` Checking our answer, we have
`6 + 6 + 9 + 9 = 30.` Therefore, the length of the rectangle is
`\boxed{9 \text{ inches}}` and the width of the rectangle is
`\boxed{30 \text{ inches}}`.

Hope that helps!