Question

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 m² 

(b) 380 m² 

(c) 384 m² 

(d) 395 m² 

Answer 1

(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 ⇒ x² = \(\frac{400\times64}{25}\) = 1024

⇒ x = 32 ⇒ AC = 32 cm and BD = 24 cm.

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

= \(\frac12\) × 32 × 24 cm² = 384 cm².