Chapter 12, Problem 7CR

a.

To determine

To calculate: The side WY if side XW is 10.

Answer to Problem 7CR

The side WY is $16.66$ .

Explanation of Solution

Given information:

Side XW = 10,

Side WZ = 6.

Formula used:

The below property is used:

The corresponding sides of similar triangles are congruent.

Calculation:

  

△XZW is similar to △WXY.

The corresponding sides of similar triangles are congruent.

  $\begin{array}{l}\frac{WZ}{WX}=\frac{WX}{WY}\\ \frac{6}{10}=\frac{10}{WY}\\ 100=6\left(WY\right)\\ WY=\frac{100}{6}=16.66\end{array}$

b.

To determine

To find: The side YZ if side WZ is 6.

Answer to Problem 7CR

The side YZ is $10.66$ .

Explanation of Solution

Given information:

Side XW = 10,

Side WZ = 6.

Formula used:

The below property is used:

The corresponding sides of similar triangles are congruent.

Calculation:

  

△HGE is similar to △EGF.

The corresponding sides of similar triangles are congruent.

  $\begin{array}{l}\frac{WZ}{WX}=\frac{WX}{WY}\\ \frac{6}{10}=\frac{10}{WY}\\ 100=6\left(WY\right)\\ WY=\frac{100}{6}=16.66\\ WY-WZ=YZ\\ YZ=16.66-6\\ YZ=10.66\end{array}$

c.

To determine

To calculate: The side XZ if side XW is 10.

Answer to Problem 7CR

The side XZ is $8$ .

Explanation of Solution

Given information:

Side XW = 10,

Side WZ = 6.

Formula used:

The below theorem is used:

Pythagoras theorem states that “In a right angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.

  

In right angle triangle,

  $a^2+b^2\text{= }{c}^2$

Calculation:

  

Side XZ can be calculated by applying Pythagoras Theorem.

In right angled triangle XZW , we get

  $\begin{array}{l}{\left(XW\right)}^2={\left(XZ\right)}^2+{\left(WZ\right)}^2\\ {\left(10\right)}^2={\left(XZ\right)}^2+{\left(6\right)}^2\\ {\left(XZ\right)}^2=100-36\\ {\left(XZ\right)}^2=64\\ XZ=\sqrt{64}=8\end{array}$