Question 93

Area of a square natural lake is 50 sq. kms. A diver wishing to cross the lake diagonally, will have to swim a distance of

Solution

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Let the side of the square lake be of length x kms.

Using pythagorus theorem, we can find the length of the diagonal as $$\sqrt{x^2+x^2}=\sqrt{2x^2}= x\sqrt{2}$$

'.' Area of the square= 50 sq. kms,

$$x^2=50$$ or x= $$5\sqrt{\ 2}$$

Therefore length of the diagonal = $$5\sqrt{\ 2}\cdot\sqrt{\ 2}=5\cdot2=10$$ km

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