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in Perimeter and Area of Plane Figures by (49.2k points)
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If the sum of the lengths of the diagonals of a rhombus of side 4 cm is 10 cm, what is its area ? 

(a) 8 cm2 

(b) 9 cm2 

(c) 10 cm2 

(d) 12 cm2 

1 Answer

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Best answer

(b) 9 cm2.

Let d1 and d2 be the lengths of the diagonals of the rhombus. 

Then,

\(\bigg(\frac{d_1}{2}\bigg)^2 + \bigg(\frac{d_2}{2}\bigg)^2= \) 4⇒ \(\frac{{d_1}^2}{4}\) + \(\frac{{d_2}^2}{4}\) = 16

⇒ d12 + d22 = 64 

⇒ (d1 +d2)2 – 2d1d2 = 64 

⇒ 102 – 2d1d2 = 64          (∴ d1 + d= 10) 

⇒ 2d1d2 = 100 – 64 = 36 

⇒ d1d2 = 18  ⇒ \(\frac12\)d1d2 = 9 cm

∴ Area of the rhombus = 9 cm2.

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