Geometry Practice Test 6

Question : 9 of 39

Marks: +1, -0

Let ABCD is a quadrilateral. Let the diagonals AC and BD meet at O. Let the perpendicular drawn from A to CD meet CD at E. Further, AO : OC = BO : OD, AB = 30 cm, CD = 40 cm and the area of the quadrilateral ABCD is 1,050

cm^2

. What is BE equal to?

30 cm
30 $√2$ cm
30 $√3$ cm
None of these

Validate

Solution:

Area of an quadrilateral triangle = 1,050

\cm^2

1050 =

1/2

(a + b) × h
1050 =

1/2

(30 + 40) × h

{1050}/{70} × 2

= h
AE = h = 30 cm.

Similarly, BF = 30 cm
⇒ ABFE is a square.
BE is the diagonal of the square.
Perimeter = 2d

√2

20 =

2d √2

{60}/√2

= d

30√2

= d
BE =

30√2

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