Area of a quadrilateral ABCD is

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

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