Question

Find the two numbers such that the mean proportional between them is 14 and the third proportional to them is 112

Answer 1

Answer:

Let the required number be x&y.

∴14is the mean proportional between x&y.

Then,

14

x

=

y

14

⇒xy=14×14=196

⇒x=

y

196

.......(1)

And given that, 112 is the third proportional to x&y.

Then, x:y::y:112

i.e.

y

x

=

112

y

⇒y

2

=112x.......(2)

Putting the value of x by equation (1) to (2) and we get,

⇒y

2

=112×

y

196

⇒y

3

=112×196

⇒y

3

=2×2×2×2×7×2×7×2×7

⇒y

3

=28×28×28

⇒y

3

=28

3

⇒y=28

Put the value of y in equation (1), and we get

x=

28

196

x=7

Hence, this is the answer.

Step-by-step explanation:

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