Question

If x is the mean proportional between 12 and 18 and y is mean proportional to 3 and 16,then x:y is equal to

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Answer 1

Given :- x is the mean proportional between 12 and 18 and y is mean proportional to 3 and 16 .

To Find :- x : y = ?

Concept used :-

if x is mean proportional between a and b then,

• x = √(ab)

Solution :-

Case 1) :- x is the mean proportional between 12 and 18 .

→ x = √(12 * 18)

→ x = √(2 * 6 * 3 * 6)

→ x = 6√(2 * 3)

→ x = 6√6

Case 2) :- y is mean proportional to 3 and 16 .

→ y = √(3 * 16)

→ y = √(3 * 4 * 4)

→ y = 4√3

then,

→ x : y = 6√6 : 4√3

→ x : y = (2 * 3 * √2 * √3) : (2 * 2 * √3)

→ x : y = 3 * √2 : 2

→ x : y = 3√2 : 2

or,

→ x : y = 3√2 : √2 * √2

→ x : y = 3 : √2

Hence, x : y is equal to 3 : √2 .

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Answer 2

From the given question the correct answer is:

 x : y = 3 : √2

Given: x is the mean proportional between 12 and 18 and y is the mean proportional to 3 and 16.

To Find: x: y =?

 The concept used:

if x is mean proportional between a and b then,

x = √(ab)

Solution :

Case 1 :- x is the mean proportional between 12 and 18 .

 x = √(12 × 18)

x = √(2 × 6 × 3 ×6)

x = 6√(2 × 3)

 x = 6√6

Case 2: y is mean proportional to 3 and 16.

y = √(3 × 16)

y = √(3 ×4 × 4)

y = 4√3

Now,

x : y = 6√6 : 4√3

x : y = (2 × 3 × √2 ×√3) : (2 × 2 ×√3)

x : y = 3 ×√2 : 2

 x : y = 3√2 : 2

Also, we can write this like

x: y = 3√2: √2 × √2

x : y = 3 : √2

Hence, x: y is equal to 3: √2 .