The question is from the topic quadrilaterals. In this problem perimeter and area of a rhombus are given and we have to find out the sum of the lengths of its diagonals. CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems. Simple Algebra combined with Geometry.
Question 16: Area of a Rhombus of perimeter 56 cms is 100 sq cms. Find the sum of the lengths of its diagonals.
Given, Perimeter = 56 and area = 100.
Let the side of the rhombus be โaโ?, then 4a = 56 => a = 14.
Area of Rhombus = Half the product of its diagonals. Let the diagonals be d1 and d2 respectively.
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) = โ1184 = 34.40
Therefore, sum of the diagonals is equal to 34.40 cm .
The question is " Find the sum of the lengths of its diagonals."
Choice B is the correct answer.
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