Chapter 4.3, Problem 31PPS

a.

To determine

Toexplain:

The pairs of congruent segments of given photo.

Answer to Problem 31PPS

The seven pairs of congruent segments are

  $\overline{AB}\cong \overline{DE},\overline{BC}\cong \overline{EF},\overline{AC}\cong \overline{DF},\overline{AB}\cong \overline{AC},\overline{DE}\cong \overline{EF},\overline{AB}\cong \overline{EF},\overline{AC}\cong \overline{DE}$

Explanation of Solution

Given information:

  

Since, $△ABC\cong △DEF$ , there are three pairs of congruent sides.

Since each triangle is isosceles, each triangle will yields two congruent legs.

Transitive property of congruence will yield another two pairs of congruent segments.

Three pairs of congruent sides are $\overline{AB}\cong \overline{DE},\overline{BC}\cong \overline{EF},\overline{AC}\cong \overline{DF}$

Congruent legs $\overline{AB}\cong \overline{AC},\overline{DE}\cong \overline{EF}$

Congruent sides resulting from transitive property $\overline{AB}\cong \overline{EF},\overline{AC}\cong \overline{DE}$

b.

To determine

To calculate:

The length of pennant string.

Answer to Problem 31PPS

The length of the pennant string is $40ft$ .

Explanation of Solution

Given information:

  

Calculation:

The length of the pennant string is equal the perimeter of the square.

The square is with $A=100f{t}^2$

Set, $s^2$ equal to $A$

  $\begin{array}{l}{s}^2=A\\ s^2=100\\ s^2=\sqrt{100}\\ s=10\end{array}$

Find the perimeter of the square,

  $\begin{array}{l}P=4s\\ =4\left(10\right)\\ =40\end{array}$

Hence, the length of the pennant string is $40ft$ .

c.

To determine

To calculate:

The total pennants will be on the string.

Answer to Problem 31PPS

The total pennants will be on the string are $80$ .

Explanation of Solution

Given information:

  

Calculation:

Each pennant takes $6in.$ of the string.

Use the conversion factor $\frac{1ft}{12in.}$ to rewrite $6in$

  $\begin{array}{l}6in=6in\times \frac{1ft}{6in}\\ =\frac{1}{2}ft\end{array}$

Hence, the number of pennants is $\frac{40ft}{\frac{1}{2}ft/pennant}=80$