The sides of a right-angled triangle forming right angle are in the ratio 5 : 12. If the area of the triangle is 270 cm², then the length of the hypotenuse is

• 39 cm

• 42 cm

• 45 cm

• 45 cm

If the measures of a diagonal and the area of a rectangle are 25 cm and 168 cm² respectively. What is the length of the rectangle?

• 31 cm

• 24 cm

• 17 cm

• 17 cm

63.

What is the length of the radius of the circumcircle of the equilateral triangle, the length of whose side is 

• 

• 6 cm

• 5.4 cm

• 5.4 cm

Three horses are tethered at 3 corners of a triangular plot of land having sides 20m, 30m and 40m each with a rope of length 7m. The area (in m²) of the region of this plot, which can be grazed  by the horses, is 

• 

• 75

• 77

• 77

If the length of a rectangle is increased in the ratio 6 : 7 and its breadth is diminished in the ratio 5 : 4 then its area will be diminished in the ratio

• 17 : 16

• 15 : 14

• 9 : 8

• 9 : 8

The perimeter of a rhombus is 60 cm and one of its diagonal is 24 cm. The area of the rhombus is

• 108 cm²

• 216 cm²

• 432 cm²

• 432 cm²

Given that the ratio of altitudes of two triangles is 4 : 5, ratio of their areas is 3 : 2. The ratio of their corresponding bases is

• 8 : 15

• 15 : 8

• 5 : 8

• 5 : 8

In triangle ABC, DE || BC where D is a point on AB and E is a point on AC. DE divides the area of Δ ABC into two equal parts. Then DB : AB is equal to

• √2 : (√2 + 1)

• √2 : (√2 - 1)

• (√2 - 1) : √2

• (√2 + 1) : √2

The diameter of each wheel of a car is 70 cm. If each wheel rotates 400 times per minute, then the speed of the car (in km/hr) is 

• 0.528

• 528

• 52.8

• 52.8

If the areas of three adjacent faces of a rectangular box which meet in a corner are 12 cm², 15cm²,  20 cm² respectively, then the volume of the box is

• 3600 cm³

• 300 cm³

• 60 cm³

• 60 cm³