The diagonals of a rhombus are mutually perpendicular and bisect each other. One diagonal is 10 cm longer than the other. If the area of the rhombus is 600 cm2, the perimeter (in cm) of the rhombus is:
100 cm
Let the shorter diagonal be \(d\) cm; then the longer one is \(d + 10\) cm.
Area of a rhombus \(= \dfrac{1}{2} d_1 d_2\), so \(\dfrac{1}{2}\, d\,(d+10) = 600\).
Then \(d^2 + 10d = 1200\), i.e. \(d^2 + 10d - 1200 = 0\).
Factor: \((d - 30)(d + 40) = 0\), giving \(d = 30\) cm. So the diagonals are 30 cm and 40 cm.
The diagonals bisect at right angles, so each side \(= \sqrt{15^2 + 20^2} = \sqrt{225 + 400} = \sqrt{625} = 25\) cm.
Perimeter \(= 4 \times 25 = 100\) cm.
Hence, the perimeter of the rhombus is 100 cm.
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