Question

The perimeters of two similar quadrilaterals are 48 cm and 60 cm, respectively. If the area of the smaller quadrilateral is 96 cm2, find the area of the larger quadrilateral.

Answer 1

perimeters in regards to ratios are one-to-one, whereas areas are squared-to-squared.

Answer 2

so the similarity ratio (the perimeter measurements) is \[\frac{ 48 }{ 60 }\]with the perimeter of the smaller in the numerator. If the area of the smaller is 96, it looks like this now when you have to find the area of the larger:

Answer 3

\[\frac{ 48 }{ 60 }=\frac{ 96 }{x }\]

Answer 4

Then cross multiply. 48 * x = 60 * 96

Answer 5

48x = 5760
x = ?

Answer 6

What you find to be x is the area of the larger figure.

Answer 7

Remember that perimeter is a one-to-one, area is a squared-to-squared, and volume is a cubed-to-cubed ratio.