Question

Adina has a rectangular garden that measures 9 m wide by 13 m long. She wants to increase the area to 192 m2 by increasing the width and length by the same amount. What will be the width (shorter dimension) of the new garden?

A.
14 m wide

B.
13 m wide

C.
12 m wide

D.
11 m wide

Answer 1

what is the area of original garden?

Answer 2

117

Answer 3

You can do this a few ways.
One way is to write an equation and solve it.

Since you are given choices, there is a much easier way.

Answer 4

117m

Answer 5

yes that is correct
so now the problem says they want to increase the area to 192...what is the difference of hte increase?

Answer 6

75

Answer 7

@JuanitaM

Answer 8

@itsannalea
While you wait for Juanita, I'll show you the easy way of solving this.

Answer 9

okay :)

Answer 10

You are told the garden will be increased by the same amount in the length and width, right?

Answer 11

yep

Answer 12

The original width is 9 m.

Look at each choice.

We'll start with A. The new width = 14 m.
The old width was 9 m. What was the increase in width in choice A.?

Answer 13

5m?

Answer 14

Right.
Since the length also has to increase by 5 m, and it was 13 m, that means the new width would become 13 m + 5 m = 18 m, right?

Answer 15

yes :)

Answer 16

sorry, my comp froze

Answer 17

I think the quickest way to do this is to set it up and factor it out

Answer 18

it's okay @JuanitaM I hate it when mine does that

Answer 19

a = lw
192 = (9+n)(13+n)

Answer 20

192 = 117 + 22n + n^2

Answer 21

Great.
Now we find the area of such a garden:
14 m * 18 m = 252 m^2
That is too big since we are looking for 192 m^2.

Now we move on to the choice B. 13 m wide

Answer 22

when you set this to zero - you will factor and get 2 numbers. disregard the negative numbers. So factor and tell me the positive number you got.

Answer 23

13 m is 4 m more than 9 m, so we add 4 m to the original length of 13 m, and we get a new rectangle that is 13 m by 17 m. Its area is 13 m * 17 m = 221 m^2.
This is also too big.

Answer 24

right.

Answer 25

Now we move on to choice C.
New width is 12 m. This is 3 m more than original width of 9 m.
Add 3 m to original length of 13 m to get 16 m.
What is 12 m * 16 m?

Answer 26

192m! :)

Answer 27

Right, since choice C gives you the right area, that is the answer.

Answer 28

thank you so much! :)

Answer 29

If this problem did not have choices, then you'd have to write an equation and solve it.
That is what Juanita is trying to tell you.
Her approach will give you the answer without guessing.

Answer 30

You're welcome.