Two rectangles, ABCD and PQRS overlap each other as shown in the figure below. Also, the overlapped area (shaded region) is 20% ¨ABCD and 33.8% of ¨PQRS. If the ratio of corresponding sides of the two rectangles is same, then ratio AD : PS equals

1.2

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1.5

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1.6

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none of these

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Solution

The correct option is D none of these

From the figure, 0.338xy = 0.2ba
ab = 1.69xy ..... (1)
Also, since ABCD and PQRS are similar, $\frac{b}{a} = \frac{y}{x} ∴ \frac{b}{y} = \frac{a}{x}$ ..... (2)
From (1) and (2), we get $\frac{a}{x}$ = 1.69 $\frac{x}{a}$
a $^{2}$ = 1.69x $^{2}$
a = 1.3x
$\frac{a}{x}$ = 1.3
answer = 1.3

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Two rectangles, ABCD and PQRS overlap each other as shown in the figure below. Also, the overlapped area (shaded region) is 20% ¨ABCD and 33.8% of ¨PQRS. If the ratio of corresponding sides of the two rectangles is same, then ratio AD : PS equals

The correct option is D none of these From the figure, 0.338xy = 0.2ba ab = 1.69xy ..... (1) Also, since ABCD and PQRS are similar,ba=yx∴by=ax..... (2) From (1) and (2), we get ax= 1.69 xa a2 = 1.69x2 a = 1.3x ax= 1.3 answer = 1.3