Chapter 6.4, Problem 11E

To determine

To Find: the ratio of the lengths of corresponding sides of figure A to figure B

Answer to Problem 11E

The ratio is $\frac{2}{3}$

Explanation of Solution

Given information: From the figure provided in the question. The length and width of the figures are:

  $\text{FG}=10\text{ft, HG = 14ft, ST = 21ft , PT = 15ft}$

Calculation:

Figures EFGH and RSPT represents a rectangle, and in a rectangle opposite sides are equal

Since, $EFGH\sim RSPT$

Therefore, ratio of corresponding sides is calculated as,

  $\frac{FG}{PT}=\frac{EH}{RS}=\frac{10}{15},\frac{HG}{ST}=\frac{EF}{RP}=\frac{14}{21}$

For similar figures the corresponding sides are equal.

  $\frac{FG}{PT}=\frac{EH}{RS}\text{= }\frac{HG}{ST}=\frac{EF}{RP}=\frac{2}{3}$

Hence. the ratio is $\frac{2}{3}$