Mathematics, 23.12.2020 17:20 kaylynn77

A rectangular pool has a sidewalk around it. The pool measures 6 feet by 10 feet and the total area of the pool and sidewalk is 96 square feet. What is the width of the sidewalk?

Answers: 3

Show answers

Answers

Answer from: shambrayperkins

A rectangular pool has a sidewalk around it. Width of the sidewalk is 1 feet.

Given

A rectangular pool has a sidewalk around it. The pool measures 6 feet by 10 feet and the total area of the pool and sidewalk is 96 square feet.

Let 'w' be the width of sidewalk

The pool measures 6 feet by 10 feet . The width of the rectangular pool with side walk is 6+x+x=6+2x

The length of the rectangular pool with side walk is 10+2x

The total area of the pool and side walk is length times width

Total area= $(6+2x)(10+2x)\\$

$96=(6+2x)(10+2x)\\96=60+32x+4x^2\\60+32x+4x^2-96=96-96\\4x^2+32x-36=0$

apply quadratic formula to solve for x

$x=\frac{-32\pm \sqrt{32^2-4\cdot \:4\left(-36\right)}}{2\cdot \:4}\\x=\frac{-32\pm \:40}{2\cdot \:4}\\x= \frac{-32+40}{2\cdot \:4}=1\\x=\frac{-32-40}{2\cdot \:4}=-9$

Width of the sidewalk cannot be negative

so the width of the sidewalk is 1 feet

Learn more : link

Answer from: lexi1268

width of the sidewalk = 1 feet

Step-by-step explanation:

Area of the pool = length × width

Length = 10 feet

Width = 6 feet

Area of the pool = length × width

= 10 feet × 6 feet

= 60 feet²

Area of the pool = 60 feet²

Total area = Area of the pool + Area of sidewalk

96 feet² = 60 feet ² + Area of sidewalk

Area of sidewalk = 96 feet² - 60 feet ²

Area of sidewalk = 36 feet²

Length of pool + sidewalk = 10 + 2x

width of pool + sidewalk = 6 + 2x

( 10 + 2 x ) ( 6 + 2 x ) -60 = 36

60 + 20x + 12x + 4x² - 60 = 36

4x² + 32x - 36 = 0

4x² + 36x - 4x - 36 = 0

4x (x + 9) -4(x + 9) = 0

(4x - 4) (x + 9) = 0

4(x - 1) (x + 9) = 0

(x - 1) = 0 (x + 9) = 0

x = 1 or x = -9

The width of the side walk can't be a negative value

Therefore, width of the sidewalk = 1 feet

Answer from: Quest

the law of definite proportions states samples of a compound will always contain the same proportion of elements by mass. in other words, a given compound will always contain the same elements in the same proportions by mass.the law of multiple proportions states when two elements combine with each other to form more than one compound, then the weights of one element that combine with a fixed weight of the other are in a ratio of small whole numbers.

Answer from: Quest

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

$\frac{2}{5}=\frac{x-18}{x}$

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so:

$\frac{2}{5}=\frac{30-18}{30}$

$\frac{2}{5}=\frac{12}{30}$

$Answer this question! eric has a riddle "i am thinking of a fraction that is equivalent to 2/5 and$

Another question on Mathematics

Mathematics, 21.06.2019 16:00

Whose conclusion is correct? choose all that apply. (two max) elijah emily edward esme

Answers: 2

Answer

Mathematics, 21.06.2019 21:00

Find the perimeter of the triangle with vertices d(3, 4), e(8, 7), and f(5, 9). do not round before calculating the perimeter. after calculating the perimeter, round your answer to the nearest tenth.

Answers: 1

Answer

Mathematics, 21.06.2019 21:30

Aye asap pls ! markin da brainiest too ! btw da step choices are all add, distribute, divide, n subtract

Answers: 2

Answer

Mathematics, 22.06.2019 00:00

What is mean median mode and range?

Answers: 2

Answer

You know the right answer?

A rectangular pool has a sidewalk around it. The pool measures 6 feet by 10 feet and the total area...