In ΔABC, the medians AD and BE meet at G. The ratio of the areas of ΔBDG and the quadrilateral GDCE is:
1 : 2
1 : 3
2 : 3
3 : 4
A.
1 : 2
As BG is the median
∴ Ar(Δ BFG) = Ar(Δ BDG) = 1 : 1 ...(i)
Ar(Δ BDG) = 1 ...(ii)
As GC is the median
∴ Ar(Δ GDC) = Ar(Δ GEC) = 1 : 1 ...(iii)
Ar(quad GDCE) = Ar(Δ GDC) + Ar(Δ GEC)
Ar(quad GDCE) = 1 + 1 = 2 ...(using (iii)) ..(iv)
From (ii) and (iv)
Ar(Δ BDG) : Ar(quad GDCE) = 1 : 2
Shashi can do a piece of work in 20 days. Tanya is 25% more efficient than Shashi. The number of days taken by Tanya to do the same piece of work is:
15
16
18
25
XYZ is a right angled triangle and ∠Y = 90°. If XY = 2.5 cm and YZ = 6 cm, then the circumradius of Δ XYZ is:
6.5 cm
3.25 cm
3 cm
2.5 cm
The length of shadow of a tower is √3 times that of its length. The angle of elevation of the sun is
45°
30°
60°
None of these
If x is the area, y is the circumference and z is the diameter of circle then the value of is
4 : 1
1 : 4
1 : 2
2 : 1