Question 21

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.

Solution

Area of rhombus = 1320

=> $$\frac{d_{1}d_{2}}{2} = 1320 => d_{1}d_{2} = 2640$$

$$ \frac{d_{1}^2}{4} + \frac{d_{2}^2}{4} =61^2$$

$$ d_{1}^2 + d_{2}^2 = 4 \times 61^2$$

$$(d_{1} + d_{2})^ 2 - 2d_{1}d_{2} = 4 \times 61^2$$

$$d_{1} + d_{2} = \sqrt{4 \times 61^2 + 2(2640)}$$ = 142

So , the answer would be option C)142 cm.

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The length of one side of a rhombus is 61 cm and its area is 1320 cm?. Find the sum of thelengths of its diagonals.