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:

this woman was an important writer and propagandist during the american revolution. she was a member of the committee of correspondence (in fact the committee was formed in her home) and was an advisor to many of the revolutionary leaders, including george washington and john adams. who was this revolutionary woman?

Find the value of each variable. write the answer in simplest radical form.

Answer from: Quest

a net is a diagram that shows a “flattened” view of a solid. in a net, each face and base is shown with all of its dimensions. a net can also serve as a pattern to build a three-dimensional solid.

a pyramid is a three-dimensional object with a base that is a polygon and triangular faces that meet at one vertex.

" the net of a triangular pyramid consists of four triangles. the base here we are given of the pyramid is a equilateral triangle, and the lateral faces are also triangles "

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