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Question 115
Gandhi Sew bridge has a pole that divides the bridge into two parts in a manner such that the ratio of the larger part to the smaller part is m : n. It is found that the ratio of the length of the bridge to the length of the smaller part is six times the ratio of the length of the larger part to the length of the bridge. Find the value of $$\sqrt{25 + mn(m^2 - 4mn + n^2)}$$.
Solution
Let us assume the lengths of the larger part of the bridge and the smaller part as mx and nx.
As per the question, $$\ \frac{mx+nx}{nx}$$ = 6$$\times\ $$ $$\ \frac{\ mx}{mx+nx}$$
This means, $$\left(m+n\right)^2$$ = 6mn
Or, $$m^2+n^2$$ = 4mn
Hence, the value of $$m^2+n^2$$ - 4mn = 0, thereby making the value of $$\sqrt{25 + mn(m^2 - 4mn + n^2)}$$ as 5.
