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The Cosmic Pool company is building a pool in Mary’s back yard. The pool is to be 8ft longer than it is wide and cover 240 square feet of the back yard. Determine both dimensions of the pool and the perimeter.
Group of answer choices

(A) Dimensions: width = 20ft & length = 12ft
Perimeter: 32ft

(B) Dimensions: width = 20ft & length = 12ft
Perimeter: 64ft

(C) Dimensions: width = 12ft & length = 20ft
Perimeter: 32ft

(D) Dimensions: width = 12ft & length = 20ft
Perimeter: 64ft

Sagot :

mhanifa

Answer:

  • (D) Dimensions: width = 12ft & length = 20ft / Perimeter: 64ft

Step-by-step explanation:

Let the length be x and width be y.

We have:

  • x = y + 8
  • Area = 240 ft²

Set equation and solve

  • xy = 240
  • y(y + 8) = 240
  • y² + 8y = 240
  • y² + 8y + 16 = 256
  • (y + 4)² = 16²
  • y + 4 = 16
  • y = 12 ft

The length is:

  • x = 12 + 8 = 20 ft

The perimeter is:

  • P = 2(x + y) = 2(20 + 12) = 2(32) = 64 ft

Correct choice is D

Let they be l and b

  • l=b+8
  • l-b=8--(1)

And

  • lb=240

So

  • (l+b)^2=(l-b)^2+4b=(8)^2+4(240)=64+960=1024
  • l+b=32--(2)

From both equations

  • 2l=40
  • l=20

And.

b=20-8=12ft

Option D

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