Question

What are a) the ratio of the perimeters and b) the ratio of the area of the larger figure to the smaller figure?

A) 5/2 and 25/4

B) 5/2 and 7/4

C) 7/2 and 25/4

D) 7/2 and 7/4

Answer 1

Given:

Base of the larger figure = 30 yd

Base of the smaller figure = 12 yd

To find:

a) The ratio of the perimeters of the larger figure to the smaller figure.

b) the ratio of the area of the larger figure to the smaller figure.

Solution:

a) We know that, the ratio of perimeters pf similar figures is equal to the ratio of their sides.

The given figures are similar. So, the ratio of the perimeters is:

$\text{Ratio of the perimeters}=\dfrac{\text{Base of the larger figure}}{\text{Base of the smaller figure}}$

$\text{Ratio of the perimeters}=\dfrac{30}{12}$

$\text{Ratio of the perimeters}=\dfrac{5}{2}$

b) The ratio of area of similar figures is equal to the ratio of squares of their sides.

$\text{Ratio of the areas}=\dfrac{\text{Base of the larger figure}^2}{\text{Base of the smaller figure}^2}$

$\text{Ratio of the areas}=\dfrac{(30)^2}{(12)^2}$

$\text{Ratio of the areas}=\left(\dfrac{30}{12}\right)^2$

$\text{Ratio of the areas}=\left(\dfrac{5}{2}\right)^2$

$\text{Ratio of the areas}=\dfrac{25}{4}$

Therefore, the correct option is A.