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In figure, ABCD and PQRC are squares such that AD = 22 cm and PC = y cm. If the area of the shaded region is $403 cm 2$ , then the value of y is:

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answer is C.

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Detailed Solution

Given that ABCD and PQRC are squares such that AD = 22 cm and PC = y cm and the area of the shaded region is

403 cm 2

In Fig. 38, A B C D and P Q R C are squares such that A D=22 cm and P C=y cm. If the area of the shaded region is 403

Area of square is

s i d e 2

.
Area of shaded region = area of big square of side 22 cm – area of small square of side y

222 − y 2 = 403 ⇒ 484 − y 2 = 403 ⇒ y 2 = 484 − 403 ⇒ y 2 = 81

⇒ y = 81 ⇒ y = 9 c m

Therefore, the value of y is 9 cm.
Hence, option 3 is correct.

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