CAT 1997 Question Paper Question 66

Question 66

In a rectangle, the difference between the sum of the adjacent sides and the diagonal is half the length of the longer side. What is the ratio of the shorter to the longer side?

Solution

Consider rectangle with shorter side as $$y$$, longer side as $$x$$ and diagonal as $$z$$.

So $$(x+y) - z = \frac{x}{2}$$ => x/2+y=z

Where $$z^2=x^2 + y^2$$

So, $$(x/2 +y)^2$$ = z

squaring on both sides and after putting value of z and solving we can get ratio of y to x as 3:4

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