By doubling each dimension, the area of a parallelogram increased from 36 square centimeters to 144 square centimeters. How do you find the percent increase in area?

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Answer 1 · 2017-07-17T16:15:42

Once you start to recognise the connections between numbers you will be able to do these much quicker than I have shown.

$color(blue)("Using shortcuts")$

$(144-36)/36xx100= 300%$

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$color(blue)("Using first principles with full explanation")$

We are only interested in the change in area. As both these values are given then anything else is a 'red herring'.

Assuming the increase is to be measured against the original area

$("change in area")/("original area")->(144-36)/36$ as a fraction, giving:

$108/36$ increase as a fraction

Notice that for 108 that $1+0+8=9$ which is divisible by 3 so 108 is also divisible by 3

Notice that for 36 that $3+6=9$ which is also divisible by 3

So to simplify we have:

$(108-:3)/(36-:3) = 36/12$

$(36-:3)/(12-:3)=(12-:4)/(4-:4)=3/1=3$
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Let the unknown value be $x$

Then we are looking to end up with $x/100$ . So by ratio

$3/1-=x/100$

To change 1 into 100 multiply by 100. What you do to the top you do to the bottom.

$(3xx100)/(1xx100) = 300/100=x/100$

So we have the percentage $300/100$ which may be written as $300%$