Algebra 2 word problem

Question

Only need a quick answer thanks!

 

I put a 3 meter by 4 meter rug in the middle of my living room, and noticed that covered exactly half the area.  If the strip of visible floor is the same width all around, what are the dimensions of my living room

Answer 1

We have a small rectangle inside of a large rectangle

 

Let x = width of uncovered strip

 

then the length of the larger rectangle will be x + 4, and x + 3 will be the width of the larger rectangle

 

since Area = Length x Width, 24m² = (x + 4)(x +3)

expanding, we get 24m² = x² + 7x + 12

 

combining, we get x² + 7x - 12m² = 0

 

since the factors of 12 are 12 and 1, 6 and 2, and 4 and 3, none of which will add up to 7, we cannot factor this expression

 

we have to use the quadratic formula (-b ± √b² - 4ac) / 2a

 

we see that a = 1, b = 7, and c = -12

so, we get (-7 ± √72 -4 • 1 • -12) / 2 • 1, which is (-7 ± √97) /2 = (-7 ± 9.84886) /2

 

we see that -7 - 9.84886 will yield a minus length, so we must discard that value.

 

which leaves (-7 + 9.84886)  / 2 = 1.4244, which is the value for x

 

Proof: (1.4244 + 3) • (1.4244 + 4) = 23.998m²

 

 

 

Answer 2

Hi Billy,

 

Quickly the answer is. . .

 

4.425  meters X 5.425 meters