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M23 : Q 24

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M23 : Q 24 [#permalink] New post 09 Oct 2010, 19:02
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If the area of a rectangle is 80, what is the angle between the diagonal of the rectangle and its longer side?

The perimeter of the rectangle is 84
The shorter side of the rectangle is 2
Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient
Statement (1) by itself is sufficient. We can find the sides of the rectangle (40 and 2).

Statement (2) by itself is sufficient. We can find the sides of the rectangle (40 and 2).

The correct answer is D.

How do we calculate the angle of the diagonal to the side of the rectangle if we only know the size of the length and breadth. Thanks in advance.
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Re: M23 : Q 24 [#permalink] New post 09 Oct 2010, 19:22
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sandhyash wrote:
If the area of a rectangle is 80, what is the angle between the diagonal of the rectangle and its longer side?

The perimeter of the rectangle is 84
The shorter side of the rectangle is 2
Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient
Statement (1) by itself is sufficient. We can find the sides of the rectangle (40 and 2).

Statement (2) by itself is sufficient. We can find the sides of the rectangle (40 and 2).

The correct answer is D.

How do we calculate the angle of the diagonal to the side of the rectangle if we only know the size of the length and breadth. Thanks in advance.


If we know the shorter and the longer side of the rectangle, we can calculate the diagonal length. By trigonometric properties: sinA = opposite side/hypotenuse we could arrive at the angle A. But since this is a D.S question, we need not worry about the angle.
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Re: M23 : Q 24   [#permalink] 09 Oct 2010, 19:22
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