Mathematics, 15.11.2019 07:31 Apple557

Arectangular pool 12 meters by 8 meters is surrounded by a walkway of width x meters. at
what value of x will the area of the walkway equal the area of the pool?

Answers: 1

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Answer from: jessicamendozacelis2

x=3 meters

Step-by-step explanation:

step 1

Find the area of the rectangular pool

A=LW

we have

$L=18\ m\\W=12\ m$

substitute

$A=18(12)=216\ m^2$

step 2

Find the area of rectangular pool including the area of the walkway

Let

x ----> the width of the walkway

we have

$L=(18+2x)\ m\\W=(12+2x)\ m$

substitute

A=(18+2x)(12+2x)

step 3

Find the area of the walkway

To find out the area of the walkway subtract the area of the pool from the area of rectangular pool including the area of the walkway

A=(18+2x)(12+2x)-216

step 4

Find the value of x if the area of the walkway equal the area of the pool

(18+2x)(12+2x)-216=216

Solve for x

$(18+2x)(12+2x)=432\\216+36x+24x+4x^{2}=432\\4x^{2} +60x-216=0$

Solve the quadratic equation by graphing

The solution is x=3 meters

see the attached figure

Arectangular pool 12 meters by 8 meters is surrounded by a walkway of width x meters. at what value

Answer from: risaroo070618

x=-4

Step-by-step explanation:

To calculate the area of the walkway, we have to subtract the total area (pool plus walkway) with the pool area. So first we calculate these two:

Pool area:

$A_{pool}=b.h=(12m)(8m)=96m^{2}$

Total area (pool plus walkway):

$A_{total}=(x+12+x)(x+8+x)=(12+2x)(8+2x)\\A_{total}=96+24x+16x+4x^{2} \\A_{total}=4x^{2}+40x+96$

Walkway area:

The walkway area is obtained by subtracting the pool are from the total area:

$A_{total}-A_{pool}=A_{walkway}$

$A_{walkway}=4x^{2}+40x+96-96=4x^{2}+40x$

Now, the problem is asking for x value that makes equal the pool area and the walkway area.

$A_{walkway}=4x^{2}+40x=96\\4x^{2}+40x-96=0\\\frac{4x^{2}+40x-96}{4} =0\\x^{2}+10x+24=0$

Now, we factorize this quadratic expression:

$x^{2}+10x+24=0\\(x+6)(x+4)=0$

Therefore,

x=-6 and x=-4

The correct answer is -4, we demonstrate this by replacing this value inside the equation for the area of the walkway:

$A_{walkway}=4x^{2}+40x=4(-4)^{2}+40(-4)=4(16)-160=64-160=-94m^{2}$

(We ignore the negative sign)

Answer from: Quest

step-by-step explanation:

4227473658779875563886538705958641728563470543621287463824132573847969p05749365273847906970680574936214

Iam stuck on this problem and am having trouble solving it. dies anyone know the steps to solving it

Answer from: Quest

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .

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