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A flat, rectangular flower bed with an area of 2,400 square
[#permalink]
05 Jun 2016, 12:32

1

Expert Reply

6

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Question Stats:

A flat, rectangular flower bed with an area of 2,400 square feet is bordered by a fence on three sides and by a walkway on the fourth side. If the entire length of the fence is 140 feet, which of the following could be the length, in feet, of one of the sides of the flower bed?

Indicate all such lengths.

A. 20

B. 30

C. 40

D. 50

E. 60

F. 70

G. 80

H. 90

_________________

Indicate all such lengths.

A. 20

B. 30

C. 40

D. 50

E. 60

F. 70

G. 80

H. 90

Show: :: OA

B, C, E, and G

Practice Questions

Question: 11

Page: 102 - 103

Question: 11

Page: 102 - 103

_________________

Sandy

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A flat, rectangular flower bed with an area of 2,400 square
[#permalink]
05 Jun 2016, 12:39

1

Expert Reply

1

Bookmarks

Explanation

Let's draw what this scenario looks like:

garden walkway one.png [ 1.47 KiB | Viewed 16798 times ]

Since we want to find possible dimensions, let's say one side has length x and the other side has length y

garden walkway two.png [ 1.68 KiB | Viewed 16788 times ]

The entire length of the fence is 140 feet

The BLUE lines represent fencing

So, we can write: x + x + y = 140

Simplify to get: 2x + y = 140

The rectangular flower bed (aka garden) has an area of 2,400 square feet

Area of rectangle = (base)(height)

We can write: xy = 2400

Which of the following could be the length, in feet, of one of the sides of the flower bed?

We have two equations:

2x + y = 140

xy = 2400

Take the TOP equation and rewrite as y = 140 - 2x

Take the BOTTOM equation and replace 140 - 2x with 140 - 2x

We get: x(140 - 2x) = 2400

Expand to get: 140x - 2x² = 2400

Rearrange to get: 2x² - 140x + 2400 = 0

Divide both sides by 2 to get: x² - 70x + 1200 = 0

Factor to get: (x - 30)(x - 40) = 0

So, EITHER x = 30 OR x = 40

So, we can already see that a side COULD have length 30 or length 40 (answer choices B and C).

However, we're not done yet!!

For each of these two possible x-values, we have y-values.

For example, one possible solution is x = 30

Since we already know that xy = 2400, we can replace x with 30 to get: 30y = 2400

Solve to get: y = 80

So, when one side has length 30, the other side has length 80.

So, 80 is another possible answer (answer choice G)

Another possible solution is x = 40

Take xy = 2400, we can replace x with 40 to get: 40y = 2400

Solve to get: y = 60

So, when one side has length 40, the other side has length 60.

So, 60 is another possible answer (answer choice E)

Answer: B, C, E, G

RELATED VIDEO

_________________

Let's draw what this scenario looks like:

Attachment:

garden walkway one.png [ 1.47 KiB | Viewed 16798 times ]

Since we want to find possible dimensions, let's say one side has length x and the other side has length y

Attachment:

garden walkway two.png [ 1.68 KiB | Viewed 16788 times ]

The entire length of the fence is 140 feet

The BLUE lines represent fencing

So, we can write: x + x + y = 140

Simplify to get: 2x + y = 140

The rectangular flower bed (aka garden) has an area of 2,400 square feet

Area of rectangle = (base)(height)

We can write: xy = 2400

Which of the following could be the length, in feet, of one of the sides of the flower bed?

We have two equations:

2x + y = 140

xy = 2400

Take the TOP equation and rewrite as y = 140 - 2x

Take the BOTTOM equation and replace 140 - 2x with 140 - 2x

We get: x(140 - 2x) = 2400

Expand to get: 140x - 2x² = 2400

Rearrange to get: 2x² - 140x + 2400 = 0

Divide both sides by 2 to get: x² - 70x + 1200 = 0

Factor to get: (x - 30)(x - 40) = 0

So, EITHER x = 30 OR x = 40

So, we can already see that a side COULD have length 30 or length 40 (answer choices B and C).

However, we're not done yet!!

For each of these two possible x-values, we have y-values.

For example, one possible solution is x = 30

Since we already know that xy = 2400, we can replace x with 30 to get: 30y = 2400

Solve to get: y = 80

So, when one side has length 30, the other side has length 80.

So, 80 is another possible answer (answer choice G)

Another possible solution is x = 40

Take xy = 2400, we can replace x with 40 to get: 40y = 2400

Solve to get: y = 60

So, when one side has length 40, the other side has length 60.

So, 60 is another possible answer (answer choice E)

Answer: B, C, E, G

RELATED VIDEO

_________________

Re: A flat, rectangular flower bed with an area of 2,400 square
[#permalink]
06 Apr 2017, 03:59

Hi, new from Australia and why not the answer is not F for bedding question?

_________________

_________________

Shopping of different sizes of bed heads aushoppinghub com/product-category/bed-heads/ online in Australia.

Retired Moderator

Joined: **07 Jun 2014 **

Posts: **4804**

WE:**Business Development (Energy and Utilities)**

Re: A flat, rectangular flower bed with an area of 2,400 square
[#permalink]
06 Apr 2017, 07:24

Expert Reply

RobCons wrote:

Hi, new from Australia and why not the answer is not F for bedding question?

Because you do not have a side equal to 70 in this case. Sides are either 30, 80 or 40, 60

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Re: A flat, rectangular flower bed with an area of 2,400 square
[#permalink]
22 May 2020, 05:49

3

1

Bookmarks

We see that the area is 2,400 and taking a quick look at the answers, we know we are working with easy integers. No fractions!

I started by taking the factors of 24

2 12

3 8

4 6

We know the perimeter of the fence is 140, so we need to find combinations of the factors that give us 140.

20(120) = 2400 = area of rectangle

20 +20 + 120 doesn't equal 140. This one's out

30 * 80 = 2400 = area of rectangle

30 + 30 + 80 = 140 A possibility!

40 * 60 = 2400 = area of rectangle

40 + 40 + 60 = 140 Another possibility!

So, now we know the possible lengths...choose from the list and you get answers B,C,E,G.

I started by taking the factors of 24

2 12

3 8

4 6

We know the perimeter of the fence is 140, so we need to find combinations of the factors that give us 140.

20(120) = 2400 = area of rectangle

20 +20 + 120 doesn't equal 140. This one's out

30 * 80 = 2400 = area of rectangle

30 + 30 + 80 = 140 A possibility!

40 * 60 = 2400 = area of rectangle

40 + 40 + 60 = 140 Another possibility!

So, now we know the possible lengths...choose from the list and you get answers B,C,E,G.

Re: A flat, rectangular flower bed with an area of 2,400 square
[#permalink]
19 Nov 2021, 22:10

shift5105 wrote:

We see that the area is 2,400 and taking a quick look at the answers, we know we are working with easy integers. No fractions!

I started by taking the factors of 24

2 12

3 8

4 6

We know the perimeter of the fence is 140, so we need to find combinations of the factors that give us 140.

20(120) = 2400 = area of rectangle

20 +20 + 120 doesn't equal 140. This one's out

30 * 80 = 2400 = area of rectangle

30 + 30 + 80 = 140 A possibility!

40 * 60 = 2400 = area of rectangle

40 + 40 + 60 = 140 Another possibility!

So, now we know the possible lengths...choose from the list and you get answers B,C,E,G.

I started by taking the factors of 24

2 12

3 8

4 6

We know the perimeter of the fence is 140, so we need to find combinations of the factors that give us 140.

20(120) = 2400 = area of rectangle

20 +20 + 120 doesn't equal 140. This one's out

30 * 80 = 2400 = area of rectangle

30 + 30 + 80 = 140 A possibility!

40 * 60 = 2400 = area of rectangle

40 + 40 + 60 = 140 Another possibility!

So, now we know the possible lengths...choose from the list and you get answers B,C,E,G.

gmatclubot

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