The following question has two statements. Study the question and the statements and decide which of the statement(s) is/are necessary to answer the question. Find the area of square ABCD if E is the mid-point of AB Statement I∶ Area of triangle ADE is 16 square meter. Statement II∶ DE = 4√5 meter.?

Option 3 : Either statement I or statement II alone is sufficient to answer the question.

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Suppose side of the square ABCD = a meter;

Since E is the mid-point of AB;

In triangle ADE;

∴ AE = a/2 and AD = a;

Statement I∶

∴ Area of ADE = a²/4

⇒ 16 = a²/4

⇒ a = 8 meter

∴ Area of square ABCD = 64 square meter

Statement II∶

DE = 4√5 meter

In the figure;

AD² + AE² = DE²

⇒ a² + a²/4 = (4√5)²

⇒ 5a²/4 = 80

⇒ a = 8 meter

∴ Area of square ABCD = 64 square meter

∴ Either statement I or statement II alone is sufficient to answer the question.