# CAT Practice : Coordinate Geometry

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Simple Algebra combined with Geometry.

## Area of the Triangle

Q.16: Area of a Rhombus of perimeter 56 cms is 100 sq cms. Find the sum of the lengths of its diagonals.
1. 33.40
2. 34.40
3. 31.20
4. 32.30

Choice (B). 34.40

## Detailed Solution

Perimeter = 56. Let the side of the rhombus be “a”, then 4a = 56 => a =14.

Area of Rhombus = Half the product of its diagonals. Let the diagonals be d1 and d2 respectively.

${\frac{1}{2} }$*d1 * d2 = 100 => d1 * d2 = 200. By Pythagoras theorem, (d1)2 + (d2)2 = 4a2 => (d1)2 + (d2)2 = 4*196 = 784.

(d1)2 + (d2)2 + 2d1 * d2 = (d1+ d2)2 = 784 +2*200 = 1184 => (d1+ d2) = √1184 = 34.40

Therefore, sum of the diagonals is equal to 34.40 cm .

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