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.

**Answers**

**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**

**Basic Concept of Ratios****Important Properties of Ratios****Ratio in Lowest Term****Types of Ratios****Comparing Ratios****Arranging Ratios****Dividing into a Given Ratio****Divide a Number into Three Parts in a Given Ratio****Dividing a Quantity into Three Parts in a Given Ratio****Problems on Ratio****Worksheet on Ratio in Lowest Term****Worksheet on Types of Ratios****Worksheet on Comparison on Ratios****Worksheet on Ratio of Two or More Quantities****Worksheet on Dividing a Quantity in a Given Ratio****Word Problems on Ratio****Proportion****Definition of Continued Proportion****Mean and Third Proportional****Word Problems on Proportion****Worksheet on Proportion and Continued Proportion****Worksheet on Mean Proportional****Properties of Ratio and Proportion**

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