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?

Jul 17, 2017

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

Explanation:

$\textcolor{b l u e}{\text{Using shortcuts}}$

(144-36)/36xx100= 300%

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$\textcolor{b l u e}{\text{Using first principles with full explanation}}$

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

$\left(\text{change in area")/("original area}\right) \to \frac{144 - 36}{36}$ as a fraction, giving:

$\frac{108}{36}$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:

$\frac{108 \div 3}{36 \div 3} = \frac{36}{12}$

$\frac{36 \div 3}{12 \div 3} = \frac{12 \div 4}{4 \div 4} = \frac{3}{1} = 3$
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Let the unknown value be $x$

Then we are looking to end up with $\frac{x}{100}$. So by ratio

$\frac{3}{1} \equiv \frac{x}{100}$

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

$\frac{3 \times 100}{1 \times 100} = \frac{300}{100} = \frac{x}{100}$

So we have the percentage $\frac{300}{100}$ which may be written as 300%