Chapter 8: Q32. (page 289)

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

Short Answer

Expert verified

The value is $x = 3 \sqrt{7}, y = 12, z = 4 \sqrt{7}$ .

Step by step solution

Step 1. Given information.

The given figure is,

Step 2. Use geometric mean concept for x.

$x$ is the geometric mean of $9$ and $7$ .

So,

$\begin{matrix} x = \sqrt{9 \cdot 7} \\ = \sqrt{3^{2} \cdot 7} \\ = 3 \sqrt{7} \end{matrix}$

Step 3. Now, Use Pythagoras Theorem in right angled triangles to find \[y\] and \[z\] :

Substitute the values and calculate.

$\begin{matrix} z^{2} = 7^{2} + {(3 \sqrt{7})}^{2} \\ z^{2} = 49 + 63 \\ z^{2} = 112 \\ z = \sqrt{4^{2} \cdot 7} .............. [takesquarerooteachside] \\ z = 4 \sqrt{7} \end{matrix}$

And,

$\begin{matrix} y^{2} = 9^{2} + {(3 \sqrt{7})}^{2} \\ y^{2} = 81 + 63 \\ y^{2} = 144 \\ y = \sqrt{144} .............. [takesquarerooteachside] \\ y = 12 \end{matrix}$

Therefore, the value is, $x = 3 \sqrt{7}, y = 12, z = 4 \sqrt{7}$ .

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

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Use geometric mean concept for x.

Step 3. Now, Use Pythagoras Theorem in right angled triangles to find \[y\] and \[z\] :

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Find the values of x,y,and z.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Use geometric mean concept for x.

Step 3. Now, Use Pythagoras Theorem in right angled triangles to find \[y\] and \[z\] :

One App. One Place for Learning.

Most popular questions from this chapter

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