Question

Noah enlarged a photograph with a scale factor of 6. The area of the enlarged photo is how many times as large as the area of the original? Answer with one number.

Answer 1

Answer:  36

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Explanation:

Let's say the original photo is 2 inches by 2 inches. The area here is 2*2 = 4.

Now lets scale up each dimension by a factor of 6. The new larger photo is now 12 inches by 12 inches (since 2*6 = 12). The new area is 12*12 = 144.

Dividing the two areas leads to 144/4 = 36 showing the new photo has 36 times more area compared to the old one.

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Here is a more general proof.

The old photo is x inches by y inches. The old area is xy.

The new photo is 6x inches by 6y inches.

We see that,

new area = 6x*6y = 6*6xy = 36xy = 36*(old area)