Question

4. What is the third proportional to 9 and
15​

Answer 1

Answer :-

• The third proportional to 9 and 15 is 25.

To find :-

• The third proportional to 9 and 15.

Step-by-step explanation :-

• Let the third proportional be "x".

• Then 9, 15 and x are in continued proportion.

We know that in a continued proportion,

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

Which means,

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

Where,

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

Here,

• First proportional = 9.
• Second proportional = 15.
• Third proportional = x.

--------------------

Hence,

$\rm \dfrac{9}{15} = \dfrac{15}{x}$

By cross multiplication,

$\rm9 \times x = 15 \times 15$

Multiplying the numbers,

$\rm9x = 225$

Transposing 9 from LHS to RHS, changing it's sign,

$\rm x = \dfrac{225}{9}$

Dividing 225 by 9,

$\overline{\boxed{\rm x = 25}}$

• So, the third proportional to 9 and 15 is 25.

-----------------------------------------------------------

Know more :-

What is proportion?

• When two ratios are equal, we say that they are in proportion.

Thus, when a : b = c : d, the quantities a, b, c and d are in proportion.