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Word Problems on Pythagoras Theorem

Pythagoras theorem states that,

In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).


(Source – Wikipedia)

The theorem can be written as,

a2 + b2 = c2

c is  hypotenuse of right triangle.

a and b are other two sides of right triangle.

Let see about some word problems by using Pythagoras theorem

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Example word problems using Pythagoras theorem:

Word problem 1:

A rectangle has a width of 4 cm and a length of 2 cm.  Find the diagonal length of the rectangle.



                        Width (a) = 4 cm

                        Length (b) = 2 cm

                        Diagonal (c) =?                     

            By using the Pythagoras theorem,

                        c2 = a2 + b2

                Substitute the value of a and b in the formula,

                        c2 = 42 + 22

                        c2 = 16 + 4

                        c2 = 20

                        c = srqt(20)

                        c = 4.47 cm

The length of diagonal is 4.47 cm

Word problem 2:

Thelength of ladder is 18 foot.  The base of the ladder is 8 feet away from the wall; find the height reached by ladder on the wall.



                                    Length of the ladder (a) = 18 foot

Distance between wall and base of ladder (b) = 8 foot

            By using the Pythagoras theorem,

                        c2 = a2 + b2

                Substitute the value of a and b in the formula,

                        c2 = 182 + 82

                        c2 = 324 + 64

                        c2 = 388

                        c = srqt(388)

                        c = 19.69 foot.

The height reached by the ladder = 19.69 foot.

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Practice word problems using Pythagoras theorem:

Practice word problem 1:

John rides his cycle 9 KM south and then 12 KM east.  Find the distance from the starting point.

Answer: 15 KM

 Practice word problem 2:

City A is 9 miles from city B, and 12 miles from city C. A road connects city B and C directly. Find the length of that road.

Answer: 15 miles.

Practice word problems 3:

Jack goes to school from his home. He walks 6 blocks east and then 8 blocks south. How far is John from the home?

Answer: 10 blokes.