A 3-foot-wide wood deck will be built around a rectangular-shaped pool

eddy2017

eddy2017

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A 3-foot-wide wood deck will be built around a rectangular-shaped pool that measures 15 feet by 30 feet. The resulting shape is also rectangular. If the lumber costs $10 per square yard, If the lumber costs 10 dollars per square yard, what is the cost of the wood for the deck.
Area of the pool
[math]A=15(ft) * 30(ft)[/math][math]A= 450 ft^2[/math]The rectangular shape has an Area of 450 ft^2
Thanks for any hint

The area of 3-ft wide wood deck is:
[math]A= 3ft × 3 ft[/math][math]A=9 ft^2[/math].

I'm stuck here.
9 ft^2 = 1 yd^2.
What to do then?
Something is wrong because 1 yd^2 yard of lumber is 10 dollars but 10 dollars is not listed as a dollars amount on choice.
 
Last edited:
eddy2017 said:
The area of 3-ft wide wood deck is:
[math]A= 3ft × 3 ft[/math][math]A=9 ft^2[/math].
Click to expand...

Incorrect!

You have done a similar problem involving grassy patch and pathway. Review that problem then:

Draw an approximate sketch. And label the sides! .... and continue...
 
eddy2017 said:
The area of 3-ft wide wood deck is:
[math]A= 3ft × 3 ft[/math][math]A=9 ft^2[/math].
Click to expand...
No, no, no. The area of the pool is indeed 450 ft^2.

Did you draw a diagram?

What are the dimensions of the pool plus deck?

If the area of the pool plus deck is x ft^2, what is the area of just the deck?
 
So the area of the pool is [math]450 ft^2[/math]
The great FIND is the cost of the wood for the deck so it seems to me the area of the pool is insignificant here, or not?
 
Thecwood deck has a width of 3 ft all around so 3 + 3 + 3 + 3 =12 ft^2
That is the perimeter of the pool
 
eddy2017 said:
The great FIND is the cost of the wood for the deck so it seems to me the area of the pool is insignificant here, or not?
Click to expand...
No. The chain of reasoning implied in your initial posts is correct. You cannot find the cost of the deck without knowing the area of the deck. Now it is true you CAN determine the area of the deck without calculating the area of the pool, but it is EASIER to use that information.
 
Can't I take 12 ft ^2 to square yards and multiply by 10 to get the cost of lumber?
 
eddy2017 said:
Thecwood deck has a width of 3 ft all around so 3 + 3 + 3 + 3 =12 ft^2
That is the perimeter of the pool
Click to expand...
Eddy

SLOW DOWN and think. If the deck ran along just one short side of the pool, it would be 15 x 3 or 45 ft^2!

Please study SK’s sketch.
 
eddy2017 said:
Thecwood deck has a width of 3 ft all around so 3 + 3 + 3 + 3 =12 ft^2
That is the perimeter of the pool
Click to expand...
incorrect!

The deck has an outer perimeter (= 2*(21+36)) and inner perimeter.(=2*(15+30))

The Uniit of perimeter is NOT ft^2 !!
 
Actually it is YOUR sketch. How do you deduce from that sketch that the dimensions are 3 x 3?
 
Subhotosh Khan said:
Incorrect!

You have done a similar problem involving grassy patch and pathway. Review that problem then:

Draw an approximate sketch. And label the sides! .... and continue...
Click to expand...
Instead of area I should have done perimeter
P

JeffM said:
Actually it is YOUR sketch. How do you deduce from that sketch that the dimensions are 3 x 3?
Click to expand...
Ok let me take a closer look.
 
Eddy

Please slow down. You are responding instantly, which means you are not stopping to think carefully about what we say.

Clearly, the question asks about the area of the deck so your ultimate goal is not the area of the pool or the inner or outer perimeter of the deck. But those things may help you find the FIND.
 
The perimeter may be expressed in millimiters, centimeter and meters.
In this case I think it would be meters,right?

Let me recap
I found the area of the pool = 450 ft
We have found the inner perimeter = 90 meters and the outside perimeter

The deck has an outer perimeter = 2*(21+36)
[math]2 (57) = 114 meters[/math].

Before we proceed.

The deck has an outer perimeter = 2*(21+36)
Where is the 21 from ?
I know why 36
30 ft + 3 feet more on either side,
But 21????

I think I am getting it
I have to find the area of the inner rectangle= l * w
=30 *15 (ft^2)
=450 ft ^2

I have the width of the deck as 3 ft
so length of the outer rectangle= 30 + ( 2*3)
= 36 ft
width of the outer rectangle =15 + (2 * 3)
=21 ft

now,
area of the outer rectangle= l* w
= 36 *21
=756 ft^2
area of the wood deck = area of outer rectangle - area of inner rectangle.
=756- 450
= 306 ft^2
but I am getting 306 ft^2
and the problem is asking for cost of a square yard.

if this okay, would i have to take 306 ft^2 to yard^2?

[math]306 ft^ to yards =34 yd^2 * 10 dollars per yard= 340 dollars[/math]the cost would be 304 dollars.

eddy2017 said:
[math]306 ft^ to yards =34 yd^2 * 10 dollars per yard= 340 dollars[/math]the cost would be 304 dollars.
Click to expand...
Great!. Thanks!
 
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