The new area will be 320 in²
<em><u>Explanation</u></em>
Lin has a drawing with an area of 20 in² and she increases all sides by a scale factor of 4.
<u>The general rule</u> we need to use here.......
"<em>If the lengths of the sides in a shape are all increased by a scale factor of , then the area will be increased by a scale factor of
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Here the sides are increased by a scale factor of 4. So, the area will be increased by a scale factor of
Thus, the new area will be:
To solve this problem, you have to know these two special factorizations:
Knowing these tells us that if we want to rationalize the numerator. we want to use the top equation to our advantage. Let:
That tells us that we have:
So, since we have one part of the special factorization, we need to multiply the top and the bottom by the other part, so:
So, we have:
That is our rational expression with a rationalized numerator.
Also, you could just mutiply by:
Either way, our expression is rationalized.