Question

The area of a ahombus is 192cm2 and one of its diagonals is 12 cm . Find the perimetre of the rhombus?

Answer 1

uhere is your answer...
the area of the Rhombus is 192cm^2
one of its diagonal is 12cm
imagine that the other diagonal is x cm
so ,the area of the Rhombus is = (1/2 × 12 × x)cm^2

According to the question,
$\frac{1}{2} \times 12 \times x = 192 \\ or \: \: 6x = 192 \\ or \: x = 32cm$
so the other diagonal is 32 cm.
the half of each diagonals will be respectively 6cm and 16cm.
we know that each diagonals intersect as 90° in Rhombus .
so,hence the sides will be
$\sqrt{ {16}^{2} + {6}^{2} } cm \\ = \sqrt{256 + 36} cm \\ = \sqrt{292} cm \\ = 17.08cm(approximately)$
so the perimeter is =(4×17.08)cm=68.32cm(ans)
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