Question

A rug is cut to fit in a room so that a border of consistent width is left on all four sides. If the room is 10 feet by 18 feet and the area of the rug is 84 feet, how wide will the border be?

Answer 1

Answer on Question #45763 – Math - Algebra

Problem

A rug is cut to fit in a room so that a border of consistent width is left on all four sides. If the room is 10 feet by 18 feet and the area of the rug is 84 feet, how wide will the border be?

Solution

Let the width of the border be $x$ feet. The area of the room is $10 \cdot 18 = 180$ (square feet). As the border width is the same on each side, we have $(10 - x)(18 - x) = 84$.

$$\begin{array}{l} 180 - 28x + x^2 = 84 \\ x^2 - 28x + 96 = 0 \\ (x - 24)(x - 4) = 0 \\ \end{array}$$

As the sides of the room are less than 24 feet each, then the right answer is 4 feet.

**Answer**: 4 feet.

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