The length of one side of a rhombus is 61 cm and its area is 1320 cm?. Find the sum of the
lengths of its diagonals.
Area of rhombus = 1320
=> $$\frac{d_{1}d_{2}}{2} = 1320 =>Â d_{1}d_{2} = 2640$$
$$ \frac{d_{1}^2}{4} + \frac{d_{2}^2}{4} =61^2$$
$$ d_{1}^2 + d_{2}^2 = 4 \times 61^2$$
$$(d_{1} +Â d_{2})^ 2 - 2d_{1}d_{2} =Â 4 \times 61^2$$
$$d_{1} + d_{2} = \sqrt{4 \times 61^2 + 2(2640)}$$ = 142
So , the answer would be option C)142 cm.
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