Answer:
a) Ratio of perimeters is 11:7
b) Ratio of area is 121:49
Step-by-step explanation:
Given : Tho similar figures with sides 22 yd and 14 yd.
We have to find
a) the ratio of the perimeters and
b) the ratio of the areas of the larger figure to the smaller figure.
Consider the given figures,
a) Since, the ratio of perimeter of similar figures is same as the ratio of the corresponding sides of the figures.
That is Ratio of perimeter is same as ratio of sides of larger figure to smaller figure .
Mathematically ,
P_1 denotes perimeter of larger figure , and P_2 denotes perimeter of smaller figure
Thus,
\frac{P_1}{P_2}= \frac{22}{14}=\frac{11}{7}
Thus, Ratio of perimeters is 11:7
b) the ratio of the areas of the larger figure to the smaller figure.
The ratio of the areas of the two similar figures is the square of the ratio of the corresponding sides.
that is
A_1 denotes area of larger figure , and A_2 denotes area of smaller figure
Thus, \frac{A_1}{A_2}= \frac{22^2}{14^2}=\frac{484}{196}=\frac{121}{49}
Thus,
\frac{A_1}{A_2}=\frac{121}{49}
Thus, Ratio of area is 121:49
