1 math world problem. Help.?

Question

A rectangular pool is 8 m longer than it is wide. A walkway 2 m wide surrounds the pool. What are the dimensions of the pool in meters if the area of the walkway is 176 m2.
A. 20 by 28
B. 16 by 24
C. 8 by 12
D. 32 by 48

i know i go that too but that isnt one of the answers.

Answer 1

Define l as the length and w as the width.

You are given that l=w+8 from the first sentence.

As for the walkway, note that the total area of the pool is l*w. Then note that the area of the pool and the walkway would be a rectangle with the length and the width 4 meters longer each (2 meters on each side of the pool). That total area of the pool and the walkway is (l+4)(w+4). The area of the walkway is the difference, or (l+4)(w+4)-lw, which we are given is 176. Using some algebra...

(l+4)(w+4)-lw=176
lw+4w+4l+16-lw=176
4w+4l+16=176
4w+4l=160
w+l=40
w+(w+8)=40 (substituting in w+8 for l using the first equation)
2w=32
w=16

l=w+8=16+8=24

The answer is (b)

Answer 2

Let x be the size of the narrower side of the pool. Then, the area of the pool is x(x + 8) (narrower side x longer side). The pool, plus the walkway, has 4 meters more in each side than just the pool (count both sides of the walkway!), so the area of pool + walkway is (x+4)(x+12).

So, the walkway only has area (x+4)(x+12) - x(x+8) = x^2 + 16x + 48 - (x^2 + 8x) = 8x+ 48.

The problem statement says that the area of the walkway is 176m^2, so

8x + 48 = 176
8(x + 6) = 176
x + 6 = 22
x = 16

So, the pool is 16 by (16 + 8), or 16 by 24.

Answer 3

pointer...you know the pool is 8 m longer than it is wide, so C or D wont work because 12 is 4 more than 8 and 48 is 16 more than 32. The only other possible answers is A or B.

To solve... draw a picture. You dont know the width of the pool, so thats n. You know the length of the pool is n + 8 (because the length is 8 longer than the width. What is the area of JUST the pool? length (n+8) times width (n).... n2+8n.

Now for the border. You know that the width of the walkway is 2 m. Look at your picture and see that the width of the whole thing (pool and walkway) is n (length of pool) + 4 (2m of walkway at top and two at bottom). Use the same concept for the length of the whole thing. You get the length is n+12.

Now... You know the area of the walkway...176. You have the formula for the area of the whole thing and the formula for the area of the pool. So if you take the area of the whole thing MINUS the area of the pool, that is the area of the walkway. You already have that, so you plug that in and solve for x.

area of whole thing - area of pool = 176
(n+12)(n+4) - (n2 + 8n)= 176
n2 +16n + 48 - n2 - 8n = 176
16n + 48 - 8n = 176
8n + 48 = 176
8n=128
n= 16

Voila!

Answer 4

First off define the pools rectange as x = width and y = length.
We have the equation y = x + 8.

Then you know that the length of the sidewalk around the pool can be defined as 2*(2y + 2x)+16. This equation is arrived at because the 2x and 2y refer to the fact that there are two sides of each, there are two lengths and two widths ect. Multiplying by two is simply because of the width of the walkway. The last part, the 16 is because there will be four corners with a 2x2 area. 2x2x4 = 16.

If you solve the second equation for x and y you get a third equation that states y + x = 40. Substitute equation one and get (x+8) + x = 40 or 2x = 32. Thus x = 16. y = x + 8, so y = 24. The correct answer is b).

Answer 5

You don't need to work anything out, you just have to use some simple reasoning.

If the pool is to fit INSIDE the perimeter of the walkway then:

Area Pool < Area walkway

And the only dimensions that you have listed that would fit inside that are C, although one side isn't 8m longer than the other.

Hope this helps

Answer 6

Pool width = w; pool length = w+8

pool area = (w)(w+8) = w^2 + 8w
walkway + pool area (w+4)(w+12) = w^2 + 16w + 48

(walkway + pool area) - (pool area) = walkway area
(w^2 + 16w + 48) - (w^2 + 8w) = 176 m^2

176 = 8w + 40
136 = 8w

w = 18 m
l = 8 + w = 16 m