Question

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

Answer 1

Answer:

Part 1) The dimensions are

Length is $20\ ft$, Width is $12\ ft$

Part 2) The perimeter is $64\ ft$

Step-by-step explanation:

Part 1) Determine both dimensions

Let

x-----> the length of the pool

y----> the wide of the pool

we know that

The area of the rectangle (pool) is equal to

$A=xy$

we have

$A=240\ ft^{2}$

so

$240=xy$ -----> equation A

$x=y+8$ ----> equation B

substitute equation B in equation A and solve for y

$240=(y+8)y$

$240=y^{2}+8y$

$y^{2}+8y-240=0$

using a graphing tool to solve the quadratic equation

the solution is

$y=12\ ft$

see the attached figure

Find the value of x

$x=y+8$ ------> $x=12+8=20\ ft$

Part 2) Find the perimeter

The perimeter of rectangle (pool) is equal to

$P=2(x+y)$

we have

$x=20\ ft, y=12\ ft$

substitute

$P=2(20+12)=64\ ft$

Answer 2

The dimensions of the pool is 12ft by 20ft and the perimeter of the pool is 64feet

How to calculate the perimeter of rectangle

The perimeter of a rectangle is calculated as;

P= 2(l+w)

where

l is the length

w is the width

If the pool is to be 8ft longer than it is wide and cover 240 square feet then the equation becomes;

240 = w(w+8)

240 = w² + 8w

w² + 8w - 240 = 0

w² +20w -12w -240 = 0

w(w+20) -12(w+20) = 0

w = 12feet

Determine the length of the rectangle. Recall that:

l = 8 + w

l = 8+12

l = 20feet

Hence the dimensions of the pool is 12ft by 20ft

Perimeter = 2(12+20)

P = 2(32)

P = 64ft

Hence the perimeter of the pool is 64feet

Learn more on area and perimeter of rectangle here; https://brainly.com/question/1143181