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Three Positive Numbers Are in the Ratio 1/2 : 1/3 : 1/4. Find the Numbers If the Sum of Their Squares is 244. - ICSE Class 10 - Mathematics

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Question

Three positive numbers are in the ratio 1/2 : 1/3 : 1/4. Find the numbers if the sum of their squares is 244.

Solution

Given, three positive numbers are in the ratio 1/2 : 1/3 : 1/4 = 6 : 4 : 3
Let the numbers be 6x, 4x and 3x.
From the given information,
(6x)2 + (4x)2 + (3x)2 = 244
36x2 + 16x2 + 9x2 = 244
61x2 = 244
x2 = 4
x = ± 2
Since, the numbers are positive, so x = 2.
Thus, the numbers are 12, 8 and 6.

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APPEARS IN

 Selina Solution for Selina ICSE Concise Mathematics for Class 10 (2018-2019) (2017 to Current)
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Ex.6A | Q: 11
Solution Three Positive Numbers Are in the Ratio 1/2 : 1/3 : 1/4. Find the Numbers If the Sum of Their Squares is 244. Concept: Quadratic Equations.
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