Here we are going to see some practice problems on pythagorean theorem.

Pythagorean Theorem Practical Problems Worksheet

(1) A man goes 18 m due east and then 24 m due north. Find the distance of his current position from the starting point? Solution

(2) There are two paths that one can choose to go from Sarahâ€™s house to James house. One way is to take C street, and the other way requires to take A street and then B street. How much shorter is the direct path along C street? (Using figure).

(3) To get from point A to point B you must avoid walking through a pond. You must walk 34 m south and 41 m east. To the nearest meter, how many meters would be saved if it were possible to make a way through the pond?

(5) The hypotenuse of a right triangle is 6 m more than twice of the shortest side. If the third side is 2 m less than the hypotenuse, find the sides of the triangle.

(6) 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. Solution

(7) The perpendicular PS on the base QR of a tiranlge PQR intersects QR at S, such that QS = 3 SR. Prove that 2PQ^{2} = 2PR^{2} + QR^{2}Solution

(8) In the adjacent figure, ABC is a right angled triangle with right angle at B and points D, E trisect BC. Prove that 8AE^{2}= 3AC^{2} + 5AD^{2}

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