In the Figure FD\AC, the area of AEF = 6sq.cm. AE = 3cm, BC = 3cm, CD = 5cm,
-
A.
(sqrt{33}) -
B.
6 -
C.
4 -
D.
2(sqrt{13}) -
E.
4(sqrt{5})
Correct Answer: Option D
Explanation
Area of triangle AEF = 6sq. cm
area of triangle = (frac{1}{2})bh (Line DX makes right angles with the parallel lines)
6 = (frac{1}{2}) x 3 x h
6 = 3h
3h = (frac{12}{3})
h = 4 = DX
From D, C x D, CX2 = 52
– 42
= 25 – 16 = 9
Cx = 3. From angle B x D, Bx = 6(i.e. 3 + 3)
BD2 = 42 + 62
= 16 + 36 = 52
BD = (sqrt{4 times 13})
= 2(sqrt{13})