Question

A pool measuring 16 meters by 20 meters is surrounded by a path of uniform​ width, as shown in the figure. If the area of the pool and the path combined is 1152 square​ meters, what is the width of the​ path?

Answer 1

Can you attach the figure? @dmoscoso

Answer 2

So I'm assuming the diagram is something like this

Answer 3

Ah okay, exactly what I was imagining it to be

Answer 4

so the area of a rectangle = length * width

the length of the pool is 20 meters
and now we added x meters on one side and x meters on the other side

the width of the pool is 16 meters
and similarly we added x meters on both sides

Answer 5

so we get the equation

(20 + x + x) * (16 + x + x) = 1152

they told us 1152 was the area of the pool and the path surrounding it

Answer 6

can you simplify what's in the parenthesis first?

Answer 7

I cant figure it out.... I'm stuck on this one :(

Answer 8

Sure! Do you understand what I've done so far? Or would you like me to begin from the beginning

Answer 9

I understand so far

Answer 10

Great!

So what is 20 + x + x

what is x + x =

Answer 11

think of it like

what is 1 apple + 1 apple

Answer 12

so I got this so far (16+2x)(20+2x)=1152

Answer 13

Good! So do you know how to multiply it

Do you know the FOIL method?

\( (a+b)(c+d) = ac + ad + bc + bd\)

Answer 14

okay so I got this 320+72x+4x^2

Answer 15

Great!! Now don't forget that it equals 1152

so let's just rearrange the terms

4x^2 + 72x + 320 = 1152

subtract 1152 on both sides so that way we can have it equal to 0
and then we can solve the quadratic equation

what do you get when you subtract 1152 on both sides?

Answer 16

11522-320=832

Answer 17

I meant 1152-320=832

Answer 18

be careful, we're subtracting 1152 from 320

so it should be

320 - 1152

Answer 19

4x^2 + 72x + 320 = 1152

4x^2 + 72x + 320 - 1152 = 1152 - 1152

4x^2 + 72x + 320 - 1152 = 0

what is 320 - 1152=

Answer 20

-832

Answer 21

Good so now we have

4x^2 + 72x -832 = 0

how do you want to solve the quadratic equation?

We can use the quadratic formula or we could even graph it

The quadratic formula is

\( x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \)

when the equation is \( ax^2 + bx + c = 0\)

Answer 22

quadratic formula

Answer 23

okay, so

a = 4
b = 72
and
c = -832

you'll have to plug it in

(if you ever want to do graphing, you can use https://www.desmos.com/calculator it's a really nice graphing website)

Answer 24

thanks for the website.

so we got x=8,-26

Answer 25

yes and so can the width be a negative number?

It's like time, can we ever have negative time? So can we ever have negative distance?

So basically, our answer is just the positive number

Answer 26

8

Answer 27

That's your width!

Answer 28

THANK YOU!!! appreciate the step by step

Answer 29

It was my pleasure!!! Also, welcome to QuestionCove!! :D

Answer 30

:)