Question

a 4 by 5 inch photo is enlarged by multiplying every dimension by 2 to form a similar 8 by 10 inch photo. What is the ratio of the perimeter of the smaller rectangle to that of the larger? What is the ratio of the two areas?

Answer 1

Although you could do it by calculating he ratios and areas, then comparing, there’s an easier way:
If every dimension is multiplied by two, every side length must also be multiplied by two, so the perimeter is doubled.
If every dimension is doubled, the new image must be both twice as wide and twice as tall as the original. Being twice as wide means having double the area, and so does being twice as tall. If these effects are combined, we conclude the area has increased by a factor of four.