Chapter 12.4, Problem 4MRE

a.

To determine

To find : Perimeter of both trapezoid.

Answer to Problem 4MRE

The perimeter of trapezoid ABCD and PQRS are 32 and 48 respectively.

Explanation of Solution

Given information :

The given trapezoids are

Calculation :

Since, the perimeter is the sum of all sides of the figure.

Therefore,

Perimeter of the trapezoid ABCD is,

  $\begin{array}{l}\text{Perimeter ABCD}=AB+BC+CD+DA\\ \text{Perimeter ABCD}=10+4+6+12\\ \text{Perimeter ABCD}=32\end{array}$

Now, perimeter of the trapezoid PQRS is,

  $\begin{array}{l}\text{Perimeter PQRS}=PQ+QR+RS+SP\\ \text{Perimeter PQRS}=15+6+9+15\\ \text{Perimeter PQRS}=48\end{array}$

Hence,

The perimeter of trapezoid ABCD and PQRS are 32 and 48 respectively.

b.

To determine

To find : The ratio of the perimeters.

Answer to Problem 4MRE

The ratio is 3 : 2.

Explanation of Solution

Given information :

The perimeter of trapezoid ABCD and PQRS are 32 and 48 respectively.

Calculation :

From part (a) the perimeter of trapezoid ABCD is 32 and PQRS is 48.

Therefore, their ratios are

  $\begin{array}{l}\frac{PQRS}{ABCD}=\frac{48}{32}\\ \frac{PQRS}{ABCD}=\frac{3}{2}\\ \frac{PQRS}{ABCD}=3:2\end{array}$

Hence,

The ratio is 3 : 2.

c.

To determine

To compare : the ratio of the perimeter to the scale factor.

Answer to Problem 4MRE

The scale factor and the ratio of the perimeter are equal.

Explanation of Solution

Given information :

The ratio of the perimeter is 3 : 3-2 and scale factor is 1.5.

Calculation :

The ratio of perimeter is 3 : 2 and scale factor is 1.5.

Since, $\frac{3}{2}$ is equivalent to 1.5.

Therefore, the scale factor and the ratio of the perimeter are equal.

Hence,

The scale factor and the ratio of the perimeter are equal.