Question

Catarina and Tom want to buy a rug for a room that is 8 by 12. They want to leave an even strip of flooring uncovered around the edges of the room. How wide a stip will have if they buy a rug with an area of 32 square feet

Answer 1

Answer:

The length of the strip is 4ft

Explanation:

Given

Room dimension: 8 by 12

Rug Area: 32

Required

Determine the width of the strip

Since it is an even strip. Represent the width with w.

So, the rug area $(in\ terms\ of\ the\ room\ dimension)$ is:

$Area = (8 - w) * (12 - w)$

Substitute 32 for Area

$32 = (8 - w) * (12 - w)$

Expand

$32 = 8(12 - w) -w(12 - w)$

Open brackets

$32 = 96 - 8w -12w + w^2$

Collect Like Terms

$w^2 - 12w - 8w -32 + 96 = 0$

$w^2 - 20w+64 = 0$

Expand

$w^2 - 16w - 4w + 64 = 0$

Factorize

$w(w - 16) - 4(w - 16) = 0$

$(w - 4)(w - 16) = 0$

$w - 4 = 0\ \ or\ w-16=0$

$w = 4\ \ or\ w=16$

But w can't be greater than the any of the dimension of the room (8 or 12).

So:

$w = 4$

Hence, the length of the strip is 4ft