Question

Find three positive numbers in the ratio 2:3:5, the sum of whose squares is 950​

Answer 1

Answer:

according to question

the numbers are

2x, 3x, 5x

then

(2x)²+(3x)²+(5x)²=950

4x²+9x²+25x²=950

38x²=950

x²=950/38

x²=25

x=5

then the numbers are

2x=10

3x=15

5x=25

Answer 2

Answer

• The numbers are 2x => 10 , 3x => 15 , and 5x => 25.

Given

• Three positive numbers are in the ratio 2 : 3 : 5.
• Sum of their square = 950.

To Find

• All the three integers.

Step By Step Explanation

Assumption :

Let us consider the numbers be 2x, 3x and 5x.

Equation :

According to the given information the equation will be ⤵

$\bigstar\: \: \underline{\boxed{ \bold{ \purple{{(2x)}^{2} + {(3x)}^{2} + {(5x)}^{2} = 950}}}}$

Solution of Equation :

Let us solve the above equation to find the value of x. So let's do it !!

$\longmapsto \sf{{(2x)}^{2} + {(3x)}^{2} + {(5x)}^{2} = 950} \\ \\\longmapsto \sf 4 {x}^{2} + 9{x}^{2} + 25 {x}^{2} = 950 \\ \\ \longmapsto \sf38 {x}^{2} = 950 \\ \\\longmapsto \sf {x}^{2} = \cfrac{ \cancel{950}}{ \cancel{38}} \\ \\\longmapsto \sf {x}^{2} = 25 \\ \\ \longmapsto \sf x = \sqrt{25} \\ \\ \longmapsto \underline{\boxed{\bold{ \green{ x = 5}}}} \: \: \: \: \dag$

Therefore, the numbers are 2x => 10 , 3x => 15 and 5x => 25.

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