SOLVING PROBLEMS INVOLVING PYTHAGOREAN THEOREM

Problem 1 :

A rectangular gate is 3 m wide and has a 3.5 m diagonal. How high is the gate?

Solution :

(3.5)2  =  x2 + 32

12.25  =  x2 + 9

x2  =  12.25 - 9

x2  =  3.25

x  =  3.25

x  =  1.8

Problem 2 :

A rhombus has diagonals of length 6 cm and 8 cm. Find the length of its sides.

Solution :

In rhombus, the diagonals will intersect each other at 90 degree.

x2  =  32 + 42

x2  =  9 + 16

x2  =  25

x  =  √25

x  =  5

So, the side length of rhombus is 5 cm.

Problem 3 :

A man rides his bicycle due east at 16 kmh-1. His son rides his bicycle due south at 20 kmh-1. If they both leave point A at the same time, how far apart are they after 4 hours?

Solution :

Time taken  =  4 hours

Distance covered  =  Time ⋅ Speed

Distance covered by bicycle in the direction east 

  =  4  16

  =  64 km

Distance covered by bicycle in the direction south 

  =  4  20

  =  80 km

x2  =  802 + 642

x2  =  6400 + 4096

x2  =  10496

x  =  102.44

they are 102 km apart 4 hours later.

Problem 4 :

An equilateral triangle has sides of length 6 cm. Find its area.

Solution :

62  =  a2 + 32

36  =  a2 + 9

a  =  √36 - 9

a  =  √27

Area of triangle  =  (1/2) ⋅ base ⋅ height

  =  (1/2) ⋅ 6  √27

  =  3√27

  =  15.6 cm2

So, area of the equilateral triangle is 15.6 cm2.

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