10th - Similar Triangles III

Class-X

Chapter- Similar Triangles

1. Which of the triangles whose sides are given below are right angled?         i)5,12,13             ii)9,12,15              iii)24,10,26
 
2.                 The sides of two triangles are given below. Select the right-angled triangle  out of these.              i)6,8,10            ii)12,13,15
 
3.        A right triangle has hypotenuse of length p cm one side of length q cm. If p-q=1, find the length of third side of the triangle.
 
4.       In ∆ ABC, BC=12 cm, CA= 16 cm and AB=20 cm. Find the value ÐC.
 
5. In ∆ABC, AD┴BC, AD=BD=5 cm. BC=17 cm. Find the value of  AC.
 
6. The foot of a ladder is a  distance of 8 m from the wall of  a house and the top of the ladder is at a height of 15 m from the  ground.Find the length of the ladder. 
7. The  heights of two vertical pillars are 7 and 12 m.The distance between their feet is 12 m.Find the distance between their tops.    
 
8. A man goes 15 m due east and then 8 m due north.How far is he from the starting point?
 
9. A 5 m long ladder is placed leaning towards a vertical wall such that it reaches the wall at a point 4 m high.If the foot of the ladder is moved 1.6 m towards the wall, then find the distance by which the top  of the ladder would slide upwards on the wall.
 
10. For going to a city B from city A, there is route via city C such that AC ^ CB, AC=2x km and CB=2(x+7) km. It is proposed to construct a 26 km highway which directly the two cities A and B.Find how much distance will be saved in reaching city  after the construction of the highway.