Question

The sum of the squares of three numbers which are in the ratio 2:3:4 is 725. Find the numbers.​

Answer 1

$\huge\bf{ \underline{ \underline{Question}}}$

• The sum of the squares of three numbers which are in ratio 2:3:4 is 725. Find the numbers.

$\huge\bf{ \underline{ \underline{Answer}}}$

• ±10 , ±15 , ±20

$\bf{ \underline{ \underline{Solution}}}$

$\sf{Let\:the\:numbers\:=\:2a,3a,4a}$

A.T.Q

$\mapsto\sf{\ (2a)^{2}+\ (3a)^{2}+\ (4a)^{2}\:=\:725}$

$\mapsto\sf{4\ a^{2}+9\ a^{2}+16\ a^{2}\:=\:725}$

$\mapsto\sf{29\ a^{2}\:=\:725}$

$\mapsto\sf{\ a^{2}\:=\:\dfrac{725}{29}}$

$\mapsto\sf{\ a^{2}\:=\:\dfrac{\cancel{725}}{\cancel{29}}}$

$\mapsto\sf{\ a^{2}\:=\:25}$

$\mapsto\sf{a\:=\:\sqrt{25}}$

$\mapsto\sf{a\:=\:±5}$

$\bf{ \underline{ \underline{So\:numbers\:are}}}$

$\bf{ \boxed{ \boxed{±10\:,\:±15\:,\:±20}}}$

$\sf{ }$

Answer 2

${\huge{\bold{\purple{\bigstar{\boxed{\boxed{\bf{Question}}}}}}}}$

• The sum of the squares of three numbers which are in the ratio 2:3:4 is 725. Find the numbers.

${\huge{\bold{\purple{\bigstar{\boxed{\boxed{\bf{Solution}}}}}}}}$

let the no. be 2x , 3x , 4x

• ATQ

$(2x)^2 + (3x)^2 + (4x)^2 = 725$

$4x^2 + 9x^2 + 16x^2 = 725$

$29 x^2 = 725$

$x^2 = \dfrac{\cancel 725}{\cancel 29}$

$x^2 = 25$

$x = \sqrt {25}$

$x = 5$

• putting value of x in 2x , 3x , 4x

2x = 2 * 5 = 10

3x = 3 * 5 = 15

4x = 4 * 5 = 20

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