The length of the sides of ∆ABC are consecutive integers. If ∆ABC has the same perimeter as an equilateral triangle with a side of length 9cm, what is the length of the shor test side of ∆ABC? 

1) 8 
2) 6
3) 4
4) 10 

To draw a pair of tange nts to a circle  which are  incline d to e ach othe r at an angle  of 45° it is re quire d to draw tange nts at the  e nd point of those  two radii of the  circle , the  angle  be twe e n which is :

1) 105° 
2) 135°
3) 145°
4) 70°

The length of each side of an equilateral triangle of area 4Ö3 cm², is 

1) 8 cm
2) 4 cm
3) Ö3 / 4 cm
4) 3 cm

A square and an equilateral triangle have equal perimeters. If the diagonal of the square is 1272 cm, then area of the triangle is 

1) 24Ö2  cm² 
2) 24Ö3 cm²
3) 48Ö3  cm²
4) 64Ö3  cm²

If the length of a median of an equilateral triangle is x cm, then its area is 

1) x² 
2) Ö3x² / 2
3) x² / Ö3
4) x² / 2