Question

Find the third proportional to the following:

`2(2)/3 m`, 4m

Answer 1

Let x be the third proportional to `2(2)/3 m`, 4m.

Third proportional to`2(2)/3 m`, 4m is the same thing as fourth proportional to `2(2)/3 m`, 4m, 4m, then

The first value is `2(2)/3 m`, which can be expressed as an improper fraction:

`2(2)/3 m = ((2 xx 3) + 2)/3m`

= `8/3m`

`8/3m` : 4m :: 4m : x

⇒ `(8/3)/4 = 4/x`

⇒ `8/3` × x = 4 × 4

⇒ `8/3x` = 16

⇒ x = 16 × `3/8`

⇒ x = `(16 xx 3)/8`

⇒ x = `48/8`

⇒ x = 6