Chapter 6.7, Problem 29E

To determine

To find : the value of $EH$ .

Answer to Problem 29E

  $EH=7\text{ m }$

Explanation of Solution

Given information :

Consider, the information provided in the question,

  $\begin{array}{l}ABCD\sim EFGH\\ EF=4\text{ m}\\ AD=21\text{ m}\\ AB=12\text{ m}\end{array}$

Calculation :

Since, $ABCD\sim EFGH$ , so ratio of corresponding sides of $ABCD$ and $EFGH$ are equal. Therefore,

  $\frac{EH}{AD}=\frac{EF}{AB}$

Here, $EF=4\text{ m}$ , $AD=21\text{ m}$ and $AB=12\text{ m}$ . Substitute these values in above equation and solve for $EH$ :

  $\begin{array}{l}\frac{EH}{21}=\frac{4}{12}\text{ (Substitute)}\\ \frac{EH}{21}\times 21=\frac{4}{12}\times 21\text{ (Multiply each side by 21)}\\ EH=7\text{ (Simplify)}\end{array}$

Hence, $EH=7\text{ m }$ .