Question 70

If $$l : m : n = 1 : 2 : 4$$, then $$\sqrt{5l^2 + m^2 + n^2}$$ is equal to:

Solution

$$l : m : n = 1 : 2 : 4$$

Let's assume $$l=y,\ m=2y\ and\ n=4y$$.

$$= \sqrt{5l^2 + m^2 + n^2}$$

$$=\sqrt{5y^2+\left(2y\right)^2+\left(4y\right)^2}$$

$$=\sqrt{5y^2+4y^2+16y^2}$$

$$=\sqrt{25y^2}$$

= 5y

= $$5l$$ [As we assumed above $$l$$ = y.]

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