Pythagoras Theorem MATHEMATICS - Pythagoras Theorem

A man goes 15 m due west and then 8 m due north. How far is he from the starting point?

A rectangular field is 40 m long and 30 m broad. Find the length of its diagonal.

The diagram shows a nest of 4 squares set one within another. The side of the outer most square is 20 cm. The midpoints of the sides are joined to give a second square and the process repeated to give the third and fourth squares. Find the length of a side of the smallest square.

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.

A ladder 13 m long rests against a vertical wall. If the foot of the ladder is 5 m from the foot of the wall, find the distance of the other end of the ladder from the ground.

Length of the sides of triangles are given. Determine which of them is a right angled triangle. In case of right angled triangle determine the hypotences
(i) 5 cm, 4 cm, 3 cm
(ii) 10 cm, 15 cm, 13 cm
(iii) 80 cm.

From the given figure, find the area of trapezium ABCD.

A ladder 15 m long reaches a window which is 9 m above the ground on one side of the street. Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window 12 m high. Find the width of the street.

A ladder 17 m long reaches the window of a building 15 m above the ground. Find the distance of the foot of the ladder from the building.

Two poles of height 9 m and 14 m stand vertically on a plane ground. If the distance between their feet is 12 m, find the distance between their tops.

Case Study: An aeroplane (P) leaves an airport (A) and flies towards north at 400 km/h. At the same time another aeroplane (Q) leaves the same airport and flies towards west at 300 km/h.

Based on the above information, answer the following questions :
Q.1. Distance covered by aeroplane P in 1.5 hours is :
(a) 600 km (b) 650 km (c) 700 km (d) 800 km
Q.2. Distance covered by aeroplane Q in 1.5 hours is :
(a) 600 km. (b) 550 km (c) 500 km (d) 450 km
Q.3. The distance between the two aeroplanes after a certain period of time is represented by the line segment :
(a) AP (b) AQ (c) PQ (d) AS
Q.4. After 1.5 hours, which aeroplane travelled longer distance and by how much?
(a) P, 150 km (b) Q, 150 km (c) P, 600 km (d) Q, 450 km
Q.5. After 1.5 hours, the distance between the two aeroplanes is :
(a) 600 km (b) 650 km (c) 700 km (d) 750 km

An aeroplane leaves an airport and flies due North at 300 km/h. At the same time, another plane leaves the same airport and flies due West at 400 km/h. After 90 minutes the distance between the two planes would be:

Hypotenuse of a right triangle is 25 cm. If out of the two legs, one is longer than the other by 5 cm, then the sum of the lengths of the legs is:

Assertion (A): In a right angled triangle, the longest side is called hypotenuse and the other two sides are called its legs. Also sum of lengths of legs is less than the length of the hypotenuse.
Reason (R): In a right angled triangle, the side opposite to the right angle is called its hypotenuse.

There are two buildings in two sides of a road. Keeping the foot of a ladder fixed at a point on the road, when it is placed on two buildings, then its top touches the buildings respectively at a height of 48 ft and 14 ft. If the length of the ladder is 50 ft, then the width of the road is: