Advertisements
Advertisements
प्रश्न
If three quantities are in continued proportion; show that the ratio of the first to the third is the duplicate ratio of the first to the second.
Advertisements
उत्तर
Let x, y and z be the three quantities which are in continued proportion.
Then, x : y :: y : z ⇒ y2 = xz ...(1)
Now, we have to prove that
x : z = x2 : y2
That is we need to prove that
xy2 = x2z
LHS = xy2 = x(xz) = x2z = RHS ...[Using (1)]
Hence, proved.
संबंधित प्रश्न
If a, b and c are in continued proportion, prove that: a: c = (a2 + b2) : (b2 + c2)
Check whether the following numbers are in continued proportion.
9, 12, 16
Verify the following:
108 : 72 : : 129 : 86
Determine if the following ratio form a proportion:
2 kg : 80 kg and 25 g : 625 kg
If a, b, c and d are in proportion, prove that: (a4 + c4) : (b4 + d4) = a2 c2 : b2 d2.
Fill the boxes using any set of suitable numbers 6 : `square` : : `square` : 15
Find the missing number in the box in the proportion:
`16/36 = square/63 = 36/square = square/117`
Sleeping time of a python in a 24 hour clock is represented by the shaded portion in the following figure.
The ratio of sleeping time to awaking time is ______.
Determine if the following are in proportion.
24, 28, 36, 48
Write True (T) or False (F) against the following statement:
8 : 9 : : 24 : 27
