Chapter 8.2, Problem 10PSB

a

To determine

To find:The ratio of lengths of corresponding sides

Answer to Problem 10PSB

The ratio of lengths of corresponding sides: 2: 3

Explanation of Solution

Given information

Quadrilateral ABCD and Quadrilateral HGFE are similar

Formula used

Ratio of sides will be same

Calculation

  $\begin{array}{l}\frac{\text{EF}}{\text{DC}}=\frac{\text{EH}}{\text{DA}}\\ \Rightarrow \text{EF}=12\times \frac{6}{9}=8\text{ units}\\ \frac{\text{HG}}{\text{AB}}=\frac{\text{EH}}{\text{DA}}\\ \Rightarrow \text{HG=15}\times \frac{6}{9}=10\text{ units}\\ \frac{\text{FG}}{\text{CB}}=\frac{\text{EH}}{\text{DA}}\\ \Rightarrow \text{FG=12}\times \frac{6}{9}=8\text{ units}\end{array}$

Now, ratios of the corresponding sides

  $\begin{array}{l}\frac{\text{EF}}{\text{DC}}=\frac{8}{12}=\frac{2}{3}=2:3\\ \frac{\text{FH}}{\text{DA}}=\frac{6}{9}=\frac{2}{3}=2:3\\ \frac{\text{HG}}{\text{AB}}=\frac{10}{15}=\frac{2}{3}=2:3\\ \frac{\text{FG}}{\text{BC}}=\frac{8}{12}=\frac{2}{3}=2:3\end{array}$

b

To determine

To calculate:The measure of line segment EF.

Answer to Problem 10PSB

The measure of EF is 8 units.

Explanation of Solution

Given information Quadrilateral ABCD and Quadrilateral HGFE are similar

Formula used

Ratio of sides will be same

Formula used Corresponding sides are equivalentCalculation$\begin{array}{l}\frac{\text{EF}}{\text{DC}}=\frac{\text{EH}}{\text{DA}}\\ \Rightarrow \text{EF}=12\times \frac{6}{9}=8\text{ units}\end{array}$:

c

To determine

To find: The perimeter of quadrilateral EFGH.

Answer to Problem 10PSB

Perimeter of EFGH is 32 units

Explanation of Solution

Given information

Quadrilateral ABCD and Quadrilateral HGFE are similar

Formula used

Ratio of sides will be same

Formula used

Perimeter is sum of all the sides of a quadrilateral

Calculation

Perimeter of quadrilateral EFGH

= EF + FG + GH + HE

= 8 + 8 + !0 + 6

= 32 units

To determine

To find:The ratio of the perimeters of quadrilaterals.

Answer to Problem 10PSB

The ratio of the perimeters of quadrilaterals is 2:3

Explanation of Solution

Given information

. Quadrilateral ABCD and Quadrilateral HGFE are similar

Formula used

Ratio of sides will be same

Formula used

Perimeter is sum of the sides of quadrilateral

Calculation

Perimeter of ABCD = 48 units

Perimeter of EFGH = 32 units

Ratio of perimeters

  $\frac{32}{48}=\frac{2}{3}=2:3$