Question

If the diagonals of a rhombus are 24 cm and 10 cm, then the area and perimeter of the rhombus are respectively 

(a) 120 sq cm, 52 cm 

(b) 240 sq cm, 52 cm 

(c) 120 sq cm, 64 cm 

(d) 240 sq cm, 64 cm

Answer 1

(a) 120 sq cm, 52 cm

Each side of the rhombus = \(\sqrt{(\frac{24}{2})^2+(\frac{10}{2})^2}\)

= \(\sqrt{12^2+5^2}\) = \(\sqrt{144+25}\) = \(\sqrt{169}\) = 13 cm

∴ Area of the rhombus = \(\frac12\) x 24 cm x 10cm = 120 cm²

Perimeter = 4 × 13 cm = 52 cm.