questions regarding area and perimeter

[shannon4]

Here are some problems that I am working on. I have the answer in a key but I'm not sure if the answer in the key is correct or if it is correct, how the answer was obtained. Thanks.

1. Original dimensions of a rectangle are: l=18, w=10. How does it affect the area if the dimensions are increased by 10%? Answer in key is 21%. I would think it is 20%.

2. Original dimensions of a square are all sides = 6. How does it affect the area if the dimensions are increased by .10 Answer in key is .21 I would think it is .20

 

[soroban]

Re: ? regarding area and perimeter

Hello, shannon4!

1. Original dimensions of a rectangle are: L = 18, W =10.
How does it affect the area if the dimensions are increased by 10%?

Don't use your "common sense" and guess at the answer . . . work it out!


The original area was: $\displaystyle \,18\,\times\,10\:=\:180$ square units.

The new length is: $\displaystyle 110\%\text{ of }18\:=\;1.10\,\times\,18\:=\:19.8$

The new width is: $\displaystyle 110\%\text{ of }10\:=\:1.10\,\times 10\:=\:11$

The new area is: $\displaystyle \,19.8\,\times\,1.1\:=\:217.8$

The increase in area is: \(\displaystyle \.217.8\,-\,180\:=\:38.7\)

The percent of increase is: $\displaystyle \,\frac{37.8}{180}\:=\:0.21\:=\:21\%$


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We could have solved this in general.

The length $\displaystyle L$ is increased by 10%; the new length is: $\displaystyle 1.1L$

The width $\displaystyle W$ is increased by 10%; the new width is: $\displaystyle 1.1W$

The new area is: $\displaystyle \,(1.1L)\,\times\,(1.1W)\:=\:1.21(LW)$

The new area is $\displaystyle 1.21$ times $\displaystyle LW$, the old area.

Therefore, the increase is: $\displaystyle 0.21\:=\:21\%$.

 

[shannon4]

Thank you!

 

[jolly]

Re: ? regarding area and perimeter

Here are some problems that I am working on. I have the answer in a key but I'm not sure if the answer in the key is correct or if it is correct, how the answer was obtained. Thanks.

1. Original dimensions of a rectangle are: l=18, w=10. How does it affect the area if the dimensions are increased by 10%? Answer in key is 21%. I would think it is 20%.

2. Original dimensions of a square are all sides = 6. How does it affect the area if the dimensions are increased by .10 Answer in key is .21 I would think it is .20

Your reasoning made no sense. In one problem, you were off by 1% and another you were off by .01. You must have had some logic. How did you arrive at those answers?

 

[jolly]

Re: ? regarding area and perimeter

Nevermind, Soroban already gave you an answer. :roll: