Question

The proportional third term of 5, 10​

Answer 1

Answer:

the proportional third term of 5, 10 ,20

Answer 2

Answer :-

• The third proportional to 5 and 10 is 20.

To find :-

• The third proportional term of 5 and 10.

Step-by-step explanation :-

• Let the third proportional term be x.

• Now 5, 10 and x are in continued proportion, because they have three proportional terms.

We know that in a continued proportion,

$\longmapsto\underline{\boxed{\sf a : b = b : c}}$

$\longmapsto \underline{\boxed{\sf \dfrac{a}{b} = \dfrac{b}{c} }}$

Where,

• a = First proportional.
• b = Mean proportional.
• c = Third proportional.

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Here,

• First proportional = 5.
• Mean proportional = 10.
• Third proportional = x.

Hence,

$\underline{\underline{\mathfrak{Substituting \: the \: given \: values,}}}$

$\longmapsto\tt \dfrac{5}{10} = \dfrac{10}{x}$

Reducing the numbers,

$\tt \longmapsto \dfrac{1}{2} = \dfrac{10}{x}$

By cross multiplication,

$\tt \longmapsto 1 \times x = 10 \times 2$

On simplifying,

$\longmapsto \underline{\boxed{\tt x = 20}}$

• Hence, the third proportional is 20.

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Know more :-

What is a ratio?

• A ratio is a comparison of measures of two or more quantities of the same kind by division.

What is a proportion?

• An equality of two ratios is called a proportion.

What is a continued proportion?

• Three quantities a, b and c (of the same kind and in same units) are said to be in continued proportion if a : b = b : c.