Question 52

If $$X : Y : Z = 1 : 2 : 3$$ and, $$X^2 + Y^2 + Z^2 = 224$$, then what is the value of $$X + Y + Z$$?

Solution

$$X : Y : Z = 1 : 2 : 3$$

let X = a, Y= 2a , Z= 3a

now $$X^2 + Y^2 + Z^2 = 224$$ = $$\left(a\right)^{2} +\left(2a\right)^{2} +\left(3a\right)^{2} = 224$$

$$a^2 + 4a^2 + 9a^2 = 224$$

$$ 14a^2 = 224$$ , $$ a^2 = \frac{224}{14}$$ , $$ a^2 = 16$$

a=4

$$X + Y + Z$$ = $$a+2a+3a= 6a $$ = $$6\times 4$$ = 24

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