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Question 7

If $$\frac{a}{c} = \frac{b}{d} = \frac{3}{4}$$ and $$\sqrt{a^2 + c^2} - \sqrt{b^2 + d^2} = 25$$, then the value of $$c - d$$ is

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Put $$a = 3k$$, $$c = 4k$$ and $$b = 3m$$, $$d = 4m$$. Then $$\sqrt{a^2 + c^2} = 5k$$ and $$\sqrt{b^2 + d^2} = 5m$$, so $$5k - 5m = 25$$ and $$k - m = 5$$. Hence $$c - d = 4k - 4m = 4 \times 5 = 20$$.

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