CAT Practice : Coordinate Geometry

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Area of rhombus is equal to the sum of the triangles contained in it.

Rhombus - Area

    Q.17: Area of a Rhombus of perimeter 56 cms is 100 sq cms. Find the sum of the lengths of its diagonals.
    1. 9*
    2. 3*
    3. 9*3
    4. 18*3


  • Correct Answer
    Choice (A). 9*

Detailed Solution

Perimeter = 12. Let the side of the rhombus be “a”, then 4a = 12 => a = 3. One angle = 120°.

Adjacent angles of a rhombus are supplementary. Therefore, the other angle = 60°.

Diagonals of a rhombus bisect each other, therefore, ∟DAC = 60°, ∟BAC =60° and ∟DCA =60° . therefore, Triangle DAC and BAC are equilateral triangles.

Therefore, Area of Rhombus = 2* Area of the Equilateral Triangle = 2 * * a2 = * 9 = 9*.

Correct Answer: 9*

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Geometry is probably the most vital topic as far as CAT preparation is concerned. Geometry sets the stage for Trigonometry, Cogeo and Mensuration as well.