Question

Cynthia Besch wants to buy a rug for a room
that is 19 ft wide and 28 ft long. She wants to
leave a uniform strip of floor around the rug. She
can afford to buy 220 square feet of carpeting.
What dimensions should the rug have?
19

Answer 1

The length and width of the rug is 20 and 11 feet respectively

The given parameters;

dimension of the room = 19 ft by 28 ft

maximum area of rug she can afford = 220 ft²

For a uniform stripe of floor around the rug, then suppose the uniform excess length of the floor to removed from each dimension = y

(28-2x)(19-2x)=220

532-94x+4x^2=220

4x^2-94x+312=0

x=39/2,4

For x=39/2, dimensions are negative.

The uniform dimension of the floor to be covered by the maximum area of rug she can afford = (28 - 4×2) and (19 -2×4 ) = 20 and 11

Thus, the dimensions of the rug should be 20 feet and 11 feet

• The area of a rectangle is length times breadth.
• Area is the total squares cm occupied by a closed figure.

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