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If the side of a rhombus is 20 metres and its shorter diagonal is three - fourths of its longer diagonal, then the area of the rhombus must be 

(a) 375 m

(b) 380 m

(c) 384 m

(d) 395 m

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(c) 384 cm2.

Let AC = x. Then BD = \(\frac{3x}{4}\)

∴ OC2 + OB2 = BC2

⇒ \(\frac{x^2}{4}\) + \(\frac{9x^2}{64}\) = 202

⇒ \(\frac{25x^2}{64}\) = 400 ⇒ x\(\frac{400\times64}{25}\) = 1024

⇒ x = 32 ⇒ AC = 32 cm and BD = 24 cm.

∴ Area of the rhombus = \(\frac12\) × AC × BD

\(\frac12\) × 32 × 24 cm2 = 384 cm2.

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