Question

A rug is to fit in a room so that a border of consistent width is left on all four sides. If the room is 15 ft by 25 ft and the area of the rug is 264 square ft, how wide will the border be? A. 1.5 ft B. 2.5 ft C. 4 ft D. 3.5 ft

Answer 1

Answer: Option 'a' is correct.

Step-by-step explanation:

Since we have given that

Dimensions of the room is given by

15 ft by 25 ft

Let x be the width around the rug.

So, new length = 15-2x

new breadth = 25-2x

Since Area of the rug = 264 sq. ft

So, it becomes,

$\text{Area of rug}=Length\times breadth\\\\264=(15-2x)(25-2x)\\\\264=375-30x-50x+4x^2\\\\264=375-80x+4x^2\\\\4x^2-80x+375-264=0\\\\4x^2-80x+111=0\\\\x=\dfrac{3}{2}\ or\ x=\dfrac{37}{2}\\\\x=1.5\ ft$

Hence, Option 'a' is correct.