# 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*${\frac{√3}{2} }$
2. 3*${\frac{√3}{2} }$
3. 9*${\surd }$3
4. 18*${\surd }$3

Choice (A). 9*${\frac{√3}{2} }$

## 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 * ${\frac{√3}{4} }$ * a2 = ${\frac{√3}{2} }$ * 9 = 9*${\frac{√3}{2} }$.

Correct Answer: 9*${\frac{√3}{2} }$

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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.