Question

Find: 1). fourth proportional to 3 6 and 4.5
2). the mean proportional btw 6.25 and 0.16
3). the third proportional to 1.2 and 1.8​

Answer 1

Solution!!

The concept of ratio and proportion has to be used here.

(1)

Let the fourth proportional to 3, 6 and 4.5 be x.

=> 3 : 6 = 4.5 : x

=> 3x = 6 × 4.5

=> 3x = 27

=> x = 9

The fourth proportional to 3, 6 and 4.5 is 9.

(2)

Let the mean proportional between 6.25 and 0.16 be x.

=> 6.25, x and 0.16 are in continued proportion.

=> 6.25 : x = x : 0.16

=> x² = 6.25 × 0.16

=> x² = 1

=> x = 1

The mean proportional between 6.25 and 0.16 is 1.

(3)

Let the third proportional to 1.3 and 1.8 be x.

=> 1.2, 1.8 and x are in continued proportion.

=> 1.2 : 1.8 = 1.8 : x

=> x = (1.8 × 1.8)/1.2

=> x = 3.24/1.2

=> x = 2.7

Hence, the third proportional to 1.3 and 1.8 is 2.7.