Question

Three numbers are in the ratio 2:3:5. If the sum of their square is 38, then find the numbers.​

Answer 1

Given

• Three numbers are in the ratio 2:3:5
• Sum of their square is 38

Explanation:

❍ Let the numbers be 2x, 3x and 5x and their sum is 38 then we can add squares of all these three numbers as:

• 2x = (2x)²
• 3x = (3x)²
• 5x = (5x)²

$\bigstar{\pmb{\underline{\sf{ According \ to \ Question :}}}} \\ \\ \colon\implies{\sf{ (2x)^2+(3x)^2+(5x)^2 = 38 }} \\ \\ \\ \colon\implies{\sf{ 4x^2 + 9x^2 + 25x^2 = 38 }} \\ \\ \\ \colon\implies{\sf{ 38x^2 = 38 }} \\ \\ \\ \colon\implies{\sf{ x^2 = \cancel{ \dfrac{38}{38} } }} \\ \\ \\ \colon\implies{\sf{ x^2 = 1 }} \\ \\ \\ \colon\implies{\sf{ x = \sqrt{1} }} \\ \\ \\ \colon\implies{\large{\pmb{\sf\green{x = 1 }}}}$

The Numbers be:-

$\\ {\sf\large{ ⍟ \ 1^{st} = 2x = 2 \times 1 \leadsto 2 }} \\ \\ {\sf\large{ ⍟ \ 2^{nd} = 3x = 3 \times 1 \leadsto 3 }} \\ \\ {\sf\large{ ⍟ \ 3^{rd} = 5x = 5 \times 1 \leadsto 5 }}$

Hence,

$\\ {\underline{\sf{The \ numbers \ are \ 2, 3, \ and \ 5. }}}$