Mathematics, 20.11.2019 07:31 july00

Arectangular pool 6 meters by 4 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

Show answers

Answers

Answer from: shanaz8199

x=1 meter

Step-by-step explanation:

step 1

Find the area of the rectangular pool

A=LW

we have

$L=6\ m\\W=4\ m$

substitute

$A=6(4)=24\ m^2$

step 2

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

Let

x ----> the width of the walkway

we have

$L=(6+2x)\ m\\W=(4+2x)\ m$

substitute

A=(6+2x)(4+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=(6+2x)(4+2x)-24

step 4

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

(6+2x)(4+2x)-24=24

Solve the quadratic equation by graphing

The solution is x=1 meter

see the attached figure

Arectangular pool 6 meters by 4 meters is surrounded by a walkway of width x meters. at what value o

Answer from: SmolBeanPotato

x = 1

Step-by-step explanation:

To answer the question we need to calculate the area of the pool and the expression of the walkway area and then make them equal.

So, the area of the pool would be:

$A_{pool}=b.h=(6m)(4m)=24m^{2}$

Then, the area os the walkway would be the difference between the whole are combines and the area of the pool. The whole are combined, pool plus walkway would be:

$A_{total}=(x+6+x)(x+4+x)=(2x+6)(2x+4)=4x^{2}+8x+12x+24=4x^{2}+20x+24$

Now, the area of the walkway is:

$A_{walkway}=A_{total}-A_{pool}\\A_{walkway}=4x^{2}+20x+24-24=4x^{2}+20x$

Then, we make equal the expression of the area of the walkway to the area of the pool, because the questions is asking the x-value when they are equal.

$4x^{2}+20x=24\\4x^{2}+20x-24=0$

Now, we solve the quadratic equation. We can extract the common factor to have an easier equation:

$4x^{2}+20x-24=0\\4(x^{2}+5x-6)=0\\x^{2}+5x-6=0$

Then, we have to find to number which multiplication results in 6 and their difference is 5. We find that the numbers are -6 and 1.

Therefore, the solutions are

x=-6;x=1

Then the solution is one, that is, if the width of the walkway is 1m it would have the same are than the pool. Also, the solution must be just the positive number, because negative lengths don't make sense.

Answer from: Quest

Ithink the answer is a

Answer from: Quest

It is 198,87032,750 + 375 = 33145 so, we take the 6% and we make it a decimal (0.6) and multiply that, then that is your answer

Another question on Mathematics

Mathematics, 21.06.2019 18:00

Olga used 100 ounces of flour to make 225 muffins. how many ounces of flour will be used to make 300 muffins?

Answers: 2

Answer

Mathematics, 21.06.2019 21:50

Which of the following is the graph of y= square root -x-3

Answers: 1

Answer

Mathematics, 21.06.2019 23:00

The value of cos 30° is the same as which of the following?

Answers: 1

Answer

Mathematics, 21.06.2019 23:30

(c) compare the results of parts (a) and (b). in general, how do you think the mode, median, and mean are affected when each data value in a set is multiplied by the same constant? multiplying each data value by the same constant c results in the mode, median, and mean increasing by a factor of c. multiplying each data value by the same constant c results in the mode, median, and mean remaining the same. multiplying each data value by the same constant c results in the mode, median, and mean decreasing by a factor of c. there is no distinct pattern when each data value is multiplied by the same constant. (d) suppose you have information about average heights of a random sample of airline passengers. the mode is 65 inches, the median is 72 inches, and the mean is 65 inches. to convert the data into centimeters, multiply each data value by 2.54. what are the values of the mode, median, and mean in centimeters? (enter your answers to two decimal places.) mode cm median cm mean cm in this problem, we explore the effect on the mean, median, and mode of multiplying each data value by the same number. consider the following data set 7, 7, 8, 11, 15. (a) compute the mode, median, and mean. (enter your answers to one (1) decimal places.) mean value = median = mode = (b) multiply 3 to each of the data values. compute the mode, median, and mean. (enter your answers to one (1) decimal places.) mean value = median = mode = --

Answers: 1

Answer

You know the right answer?

Arectangular pool 6 meters by 4 meters is surrounded by a walkway of width x meters. at what value o...

Questions