Question

11. Find three positive numbers in the ratio 2:3:5, the sum of whose squares is 950.
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Answer 1

Answer:

• Let a:b:c = 2:3:5
• then, a = 2x

b = 3x

c = 5x

• Now given that, a^2 + b^2 + c^2 = 950
• implies, (2x)^2 + (3x)^2 + (5x)^2 = 950
• i.e., 4x^2 + 9x^2 + 25x^2 = 950
• i.e., 38x^2 = 950
• By solving we will get, x = 5

So, the three positive numbers are,

a = 2x = 2×5 = 10

b = 3x = 3×5 = 15

c = 5x = 5×5 = 25

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Answer 2

Answer:

10:15:25

Step-by-step explanation:

Let a:b:c=2:3:5

a=2x,b=3x,c=5x

(2x)∧2+(3x)∧2+(5x)∧2=950

4x∧2+9x∧2+25x∧2=950

38x∧2=950

x=5

So the three positive numbers are:

a=2x=2(5)=10

b=3x=3(5)=15

c=5x=5(5)=25