Question

If x,9,y,16 are in continued proportion, then 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 :

The given continued proportion are x, 9, y, and 16

Now to find the values of x and y :

Since x, 9, y, and 16 are in continued proportion

We can write it as

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

∴ $\frac{9}{y}=\frac{y}{16}\hfill (1)$

and $\frac{x}{9}=\frac{9}{y}\hfill (2)$  

From (1) $\frac{9}{y}=\frac{y}{16}$

we have that $y^2=144$

∴ y=12

From (2) $\frac{x}{9}=\frac{9}{y}$ , we get

$xy=81$

Now substitute the value of y in the above equation we get,

x(12)=81

$x=\frac{81}{12}$

∴ $x=\frac{27}{4}$

∴ the values of x and y are $\frac{27}{4}$ and 12 respectively.

           

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Answer 2

Answer:

Q12. If x ,4, 16 are in continued-proportion, then the value of x is