Question

The perimeter of the rectangle whose length is 60 cm and a diagonal is 61 cm is

(a) 120 cm (b) 122 cm (c) 71 cm (d) 142 cm

Answer 1

(d) Let ΔBCD be the given rectangle such that AB = CD = 60 cm and AC = 61 cm.

In ΔABC,

(AC)² = (AB)² + (BC)²

⇒ (61)² = (60)² + (BC)²

⇒ (BC)² = 3721 – 3600 = 121 = 11²

⇒ BC = 11 cm

∴ Perimeter of rectangle ABCD = 2(AB + BC)

= 2 (60 + 11) = 2(71) = 142 cm