Question:
Area of a quadrilateral ABCD is 20 cm2 and perpendiculars on BD from opposite vertices are 1 cm and 1.5 cm. The length of BD is
(a) 4 cm
(b) 15 cm
(c) 16 cm
(d) 18 cm
Solution:
The correct answer is option (c) 16 cm
Explanation:
Given that, the area of a quadrilateral = 20 cm2
We know that, the area of a quadrilateral = (1/2) (diagonal) (sum of the altitudes)
20 = (1/2) (1+1.5) BD
20 = (1/2) (2.5) BD
20×2 = 2.5 BD
40 = 2.5 BD
BD = 16 cm