Question

Find two numbers such that their mean proportional is 28 and third proportional in 224.

Answer 1

Let x and y be two given numbers.

Mean proportional of x and y is 28.

`sqrt(xy)` = 28

xy = 28² = 784   ...(1)

If 224 is the third proportional,

Then,

x : y = y : 224

⇒ `x/y = y/224`

⇒ x × 224 = y²

⇒ y² = 224x   ...(2)

Substitute equation (1) into (2)

xy = 784

x = `784/y`

Substitute in equation (2):

y² = 224`(784/y)`

y³ = 224 × 784

y³ = 175616

y = `root3 (175646)`

y = 56

Now find x:

x = `784/56`

= 14

The two numbers are 14 and 56.