Question

A carpet is laid on floor of a room 8 m by 5 m. There is border of constant width all around the carpet. If the area of the border is 12m² find its width.

Answer 1

Let the width of the border be x m.

The length and breadth of the carpet are 8 m and 5 m, respectively.

Area of the carpet = 8 x 5 = 40m²

Length of the carpet without border = (8 - 2x)

Breadth of carpet without border = (5 - 2x)

Area of the border 12 m²

Area of the carpet without border = (8 - 2x)(5 - 2x)

Thus, we have:

\(\Rightarrow x=\frac{1}{2}\) and \(x=6\)

Because the border cannot be wider than the entire carpet, the width of the carpet is \(\frac{1}{2}m,\) i.e., 50 cm.