Question

In Fig. 38, ABCD and PQRC are squares such that AD = 22 cm and PC = y cm. If the area of the shaded region is 403 cm²,
then the value of y is

(a) 3 (b) 6 (c) 9 (d) 10

Answer 1

Here, AD = 22 cm.
Area of square ABCD = (22)² cm² = 484 cm²
Area of square PQRC = y² cm²
Now, as per the question
Area of shaded region = Area of square ABCD − Area of square PQRC
$$\begin{gathered} 403=484-y^2 \\ \Rightarrow y^2=484-403=81 \\ \Rightarrow y=9 \end{gathered}$$
Hence, the correct option is (c).