Question

if x,9,y,16 are in continued proportion , find the value of x and y​

Answer 1

Given:

• x,9,y,16 are in continued proportion.

To Find:

• The value of x and y.

Solution:

x,9,y,16 are in continued proportion.

Now, write in continuation form

$\: \sf \frac{x}{9} = \frac{9}{y} = \frac{y}{16}$

$\sf\therefore$9/y = y/16 -----(i)

and x/9 = 9/4 --------(ii)

From(i)9/y = y/16

$\: \sf \: y \times y = 9 \times 16 \\ \\ \: \: \sf {y}^{2} = 144 \\ \\ \: \sf y = \sqrt{144} \\ \\ \: \sf \therefore y = 12$

From(ii) x/9 = 9/y

$\: \sf x \times y = 9 \times9 \\ \\ \: \: \sf \therefore\: xy = 81$

Now, substitute the value of y here

$\: \sf \: x \times y = 81 \\ \\ \: \sf \: x \times 12 = 81 \\ \\ \: \: \sf \: x = \frac{81}{12} \\ \\ \: \: \sf \therefore \: x = \frac{27}{4}$

The values of x and y are 27/4 and 12 respectively.

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