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The following question has two statements. Study the question and the statements and decide which of the statement(s) is necessary to answer the question. In square ABCD, AB = 8 cm. Which statement assures that area of square PQRS is exactly half of the area of square ABCD? I) AC = PQ II) PQ + QR + RS + PS = 2(AC)

The following question has two statements. Study the question and the statements and decide which of the statement(s) is necessary to answer the question. In square ABCD, AB = 8 cm. Which statement assures that area of square PQRS is exactly half of the area of square ABCD? I) AC = PQ II) PQ + QR + RS + PS = 2(AC) Correct Answer Only II

Side of square ABCD = 8 cm

Diagonal of square ABCD = AC = side × √2 = 8√2 cm

⇒ Area(ABCD) = 82 = 64 cm2

Considering statement I,

⇒ PQ = AC = 8√2 cm

⇒ Area (PQRS) = (8√2)2 = 128 cm2

⇒ The area of PQRS is not the half of the area of ABCD

Considering statement II,

⇒ PQ + QR + RS + PS = 2(AC) = 2(8√2) = 16√2 cm

As all sides of square are equal,

⇒ PQ = 16√2/4 = 4√2 cm

⇒ Area(PQRS) = (4√2)2 = 32 cm2

⇒ The area of PQRS is exactly half the area of ABCD

∴ Only II is sufficient to answer the question

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