Question

four numbers are in proportion . their extreme terms are 2 and 54. one of the middle term is thrice the othere one .find the middle terms

Answer 1

product of means = product of extremes
3x×x=2×54
3x^2=108
x^2=108÷3
x^2=36
x=6

3x=3×6
=18

Answer 2

Concept:

Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal.

An equation known as proportion shows that the two ratios presented are equal to one another. For instance, the time it takes a train to travel 100 kilometres per hour is equal to the time it needs to travel 500 kilometres in five hours. Example: 100 km/hr = 500 km/5 hour.

product of means = product of extremes

Given:

Four numbers are in proportion . their extreme terms are 2 and 54. one of the middle term is thrice the other one

Find:

Find the middle terms

Solution:

Let the middle term be x

So, the other number be 3x

Proportion: 2:3x::x:54

product of means = product of extremes

3x×x=2×54

3x²=108

x²=108/3

x²=36

x=6

3x=3×6

    =18

Therefore, the middle term be  6 and 18

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