SOLUTION: Lawrence is increasing his rectangular patio in his backyard. His patio is currently 12 feet by 10 feet. He wants to increase the patio by adding a decorative tile the same width (

Question 1206274: Lawrence is increasing his rectangular patio in his backyard. His patio is currently 12 feet by 10 feet. He wants to increase the patio by adding a decorative tile the same width (x) all the way around creating a total area of 180 square feet. Select all the quadratic equations that represent Lawrence’s new patio area.
A x^2 + 11x − 15 = 0
B x^2 − 11x − 15 = 0
C x^2 + 22x − 60 = 0
D x^2 − 22x − 60 = 0
E 4x^2 + 44x − 60 = 0
 4xx2 − 44xx − 60 = 0
Found 6 solutions by josgarithmetic, greenestamps, mananth, MathTherapy, ikleyn, math_tutor2020:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Dimensions of new patio, increased area with the tiled part

****************MISTAKEN INTERPRETATION IN SET-UP***********
****************NEED PLUS. NOT MINUS***********************
square feet total area; simple algebra from here.

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

I'm not sure what the other tutor was thinking when they wrote their response. If the current dimensions are 12 feet by 10 feet and the patio area is increased by a uniform border of width x, then the increased dimensions are not 12-2x and 10-2x....

Correct setup....

ANSWER: A

Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
Original dimensions 12 by 10
width of tile is x ft
The length increases to (12+2x) ............x on each side
The width increases to 10+2x
Area of the new patio (12+2x)(10+2x) which is 180 ft^2
(12+2x)(10+2x)=180
120+24x+20x+4x^2=180
4x^2 +44x-60=0
divide by 4
x^2+11x-15=0

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Lawrence is increasing his rectangular patio in his backyard. His patio is currently 12 feet by 10 feet. He wants to increase the patio by adding a decorative tile the same width (x) all the way around creating a total area of 180 square feet. Select all the quadratic equations that represent Lawrence’s new patio area. A x^2 + 11x − 15 = 0 B x^2 − 11x − 15 = 0 C x^2 + 22x − 60 = 0 D x^2 − 22x − 60 = 0 E 4x^2 + 44x − 60 = 0  4xx2 − 44xx − 60 = 0 (12 + 2x)(10 + 2x) = 180 FOIL and simplify to form a quadratic equation. Correct answer: CHOICES A & E

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

It is incorrect to ask which of these equations represents the area.

No one of these equations, literally speaking, represents the area.

Mathematically correctly is to say that equations A and E are correct equations
for the width x of the added strip.

Yes, some of these equations originate from the equation for the area,
but after transformations, they just do not represent the area.

.............................

Please don't think that I'm picking on words.

My writing is just the CORRECT mathematical verbal formulation.

Don't curse me, just learn from me.

It is why and for what you come to this forum.     ( <<<--- just in case if you do not understand for what and why you come here).

Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Refer to my previous solution found here
https://www.algebra.com/algebra/homework/quadratic/Quadratic_Equations.faq.question.1205624.html
If you have further questions then please let me know.

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