Geometry Problem!

[Videoorchard]

Hey,

I have a question regarding Geometry. Kindly look at the problem below!

Question:
Ten 8 Foot long poles will be arranged in a rectangle to surround a flower bed

Qty A:
The area in square feet of the flower bed.

Qty B:
300

Doubt:
Generally we calculate area of rectangle as width x height. So in this case, width and height=8, so that would be 8 x 8=64 isn't it? Why did the author represent height and width as (2x8)(3x8)=384? Could you please draw the distinction between the above 2 methods?

Source:
Geometry Strategy Guide
Chapter 2, Problem 2

[n00bpron00bpron00b]

Easy to explain with drawing but I'll try :)

Area of rectangle = length x width

The question states we have 10 poles in total and each is of height 8 units.

You could arrange 10 poles in multiple configuration. Just imagine street light poles and rotate them in such way that they lie flat horizontally along the ground.

Case 1 - (each line ("-") & ("|") represents one pole of length 8 units)

- - - -
| Rec |
- - - -

Length: 4 flat lines (i.e 4 poles) each of length 8 units => total length = 8x4 = 32

Width: 1 flat line (i.e. 1 pole) each of length 8 units => total width = 8x1 = 8

Total area length x width = 32 x 8 = 256

In this case quantity (B) is greater

Case 2: Similarly imagine 3 poles for the length (3 flat lines) & 2 poles for the width (2 flat lines)

Length = 3 poles of each length 8 = 8x3 =24
width = 2 poles of each length 8 = 8x2 = 16

Total area = length x width = 24 x 16 = 384

Quantity (A) is greater

Hence (D)

Remember, we have to utilize all 10 poles. (8x8 = 64 ; cannot be the case)

[tommywallach]

Great response from noob,

Looks like the overall mistake here was missing the fact that we have 10 rods. One other thing though, remember that a real GRE question would never simply ask you to calculate the area of a basic rectangle. There would always be something else going on, so make sure you're looking for it!

-t

[Videoorchard]

Hello,

Thank you for answering Mr.Wallach and Noob! :)

Regarding the above problem, i have a quick question. If you look at quantity A, Isn't the problem asking you for the area of "Flower bed" as opposed to the area of the surrounding rectangle? The poles arranged in the rectangular fashion, "covers/surrounds" the flower bed! Now, the flower bed comes in different forms: circles/rectangular etc..The question doesnot specify what so ever how the flower bed looks like! :D Rectangular(In which case the question is valid),Circular(Question becomes invalid)!

Flower bed:
http://goo.gl/FFlcJZ

[n00bpron00bpron00b]

1) Question : Ten 8 Foot long poles will be arranged in a rectangle to surround a flower bed (question states that the flower bed is rectangle in shape)

2) Perimeter : border that surrounds the object - gives it an definite shape (in this case poles form the perimeter of the flower bed)

For Circle : circumference is the perimeter

3) Area: Portion inside the boundary (i.e. perimeter)

Now,

Isn't the problem asking you for the area of "Flower bed" as opposed to the area of the surrounding rectangle?

- - - -
| bed |
- - - -

The flower bed itself is a rectangle, there are no two different components. You can either call the entire object (as a whole) a rectangle (in generic terms) or a flower bed (special name given in the problem). So basically, what you have stated above "Area of flower bed" & "Area of rectangle" both imply the same.

Hope this helps.

[tommywallach]

Thanks, Noob!

-t

[Videoorchard]

Thank you noob for furthur elucidating! :) The explanation made the concept more clearer! thank you!

[tommywallach]

That guy knows his stuff!