Question
The area of a rhombus is given as 384 cm², and its
perimeter measures 80 cm. Determine the total length of its two diagonals.Solution
Length of each side of the rhombus = 80 ÷ 4 = 20 cm
Let the length of longer diagonal be '2x' cm and that of smaller diagonal be '2y' cm.
So, (1/2) X 2x X 2y = 384
Or, xy = 192 
Now, since the diagonals of a rhombus are perpendicular bisectors of each other. So, ABC is a right angled triangle.
And, in triangle ABC, we have
x2 + y2 = 400
Since, (x + y)2 = x2 + y2 + 2xy
So, (x + y)2 = 400 + 2 X 192
Or, (x + y)2 = 784
So, x + y = 28
So, required sum = 28 X 2 = 56 cm
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