# Worksheet on Mean Proportional

Practice the questions given in the worksheet on mean proportional.

1. Find the mean proportional of the following sets of positive numbers:

(i) x$$^{3}$$y, xy$$^{3}$$

(ii) (x - y)$$^{2}$$, (x + y)$$^{3}$$

2. Find the mean proportional of the following:

(i) 9, 16

(ii) 4$$\frac{4}{7}$$, 3$$\frac{1}{2}$$

(iii) (a + b)(a - b)$$^{3}$$, (a + b)$$^{3}$$(a - b)

(iv) $$\frac{x^{2}}{4ab}$$, $$\frac{a}{by^{2}}$$

3. Find the mean proportional between

(i) 5 and 45

(ii) 0.04 and 0.0036

(iii) 0.25 and 6.25

4. Find the third proportional of the following:

(i) 0.5, 0.25

(ii) a$$^{2}$$b, ab$$^{2}$$

(iii) $$\frac{x}{y}$$ + $$\frac{y}{x}$$, $$\frac{x}{y}$$

5. (i) If the mean proportional of a and c is b then prove that a, c, a$$^{2}$$ + b$$^{2}$$ and b$$^{2}$$ + c$$^{2}$$ are proportional.

(ii) If b is the mean proportional of a and c, prove that the mean proportional of a$$^{2}$$ + b$$^{2}$$ and b$$^{2}$$ + c$$^{2}$$ is ab + bc.

(iii) If b is the mean proportional of a and c, prove that

$\left ( \frac{ab + bc + ca}{a + b + c} \right )^{3} = abc$

Answers for the worksheet on mean proportional are given below.

1. (i) x$$^{2}$$y$$^{2}$$

(ii) x$$^{2}$$ - y$$^{2}$$

2. (i) 12

(ii) 4

(iii) $$(a^{2} - b^{2})^{2}$$

(iv) $$\frac{x}{2by}$$

3. (i) 15

(ii) 0.012

(iii) 1.25

4. (i) 0.125

(ii) b$$^{3}$$

(iii) $$\frac{x^{3}}{y(x^{2} + y^{2})}$$

● Ratio and proportion

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