# 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

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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.