Chapter 8: Q35. (page 289)

Find the values of $x, y,$ and $z$ .

Short Answer

Expert verified

The value is, $x = \frac{27}{5}, y = \frac{48}{5}, z = \frac{36}{5}$ .

Step by step solution

Step 1. Given information.

The given figure is,

Step 2. Concept used.

The small right triangle with base \[x\] is similar to the large right triangle.

So,

$\begin{matrix} \frac{9}{15} = \frac{x}{9} \\ 9^{2} = 15 x [multiplyeachsideby15 \cdot 9] \\ x = \frac{81}{15} [divideeachsideby15] \\ x = \frac{27}{5} \end{matrix}$

$\begin{matrix} x + y = 15 \\ y = 15 - x [subtractxfromeachside] \\ y = 15 - \frac{27}{5} \\ y = \frac{48}{5} \end{matrix}$

Step 3. Use geometric mean concept.

z is the geometric mean of x and y .

$\begin{matrix} z = \sqrt{x \cdot y} \\ z = \sqrt{\frac{27}{5} \cdot \frac{48}{5}} \\ z = \frac{36}{5} \end{matrix}$

Therefore, value is $x = \frac{27}{5}, y = \frac{48}{5}, z = \frac{36}{5}$ .

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Find the values of $x, y,$ and $z$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept used.

Step 3. Use geometric mean concept.

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Find the values of x,y,and z.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept used.

Step 3. Use geometric mean concept.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

Find the values of $x, y,$ and $z$ .