Chapter 7.3, Problem 23WE

To determine

To find: The property of proportion that can be applied for representing that ratio of perimeters of given figures is equal to the ratio of its any two corresponding sides.

Answer to Problem 23WE

Required ratio applied to show the ratio of two perimeters equal to ratio of any two corresponding sides is, “If

  $\frac{a}{b}=\frac{c}{d}=\frac{e}{f}=\mathrm{...}$ , then $\frac{a+c+e+\mathrm{...}}{b+d+f+\mathrm{...}}=\frac{a}{b}=\mathrm{....}$ ”.

Explanation of Solution

Given information: Two figures are given so that ratio of their perimeters have to show equal to the ratio of their any corresponding sides, using a property of proportion.

Concept used: Perimeter of a figure is the sum of its all sides. Also, property of proportion says that if different ratios are equal, then the ratio of sum of their numerators and denominators separately are also equal to each other.

Calculation: Let the four sides of first figure be a,c,e and g and their corresponding sides in second figure are b,d,f and h, then perimeter of first figure is $a+c+e+g$ and perimeter of second figure is $b+d+f+h$ .So, by property of proportion, if, $\frac{a}{b}=\frac{c}{d}=\frac{e}{f}=\mathrm{....}$

then, $\frac{a+c+e+g}{b+d+f+h}=\frac{a}{b}=\frac{c}{d}=\frac{e}{f}=\frac{g}{h}$

Conclusion: Thus, second property of proportion shows that the ratio of perimeter of any two figures is equal to the ratio of their corresponding sides of both figure.