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Knowledge Desk

Pythagoras of Samos was an ancient Ionian Greek philosopher and the eponymous founder
of Pythagoreanism. He was born on the island of Samos, Greece in 569 BC. Pythagoras was well
educated, and he played the lyre throughout his lifetime. Pythagoras was most famous for his
alleged mathematical discoveries. Pythagoras has commonly been given credit for discovering
the Pythagorean Property, sum of the angles of a triangle, etc.

Example 14: A 17 m long ladder leans against a wall. If the foot of the ladder is 8 m away from the
foot of the wall, find how far up the wall, the ladder reaches.
Solution: Let AC be the ladder which leans against the wall BD and 8 m away from the foot of the wall.
AC = 17 m, AB = 8 m.
2
2
2
Now, AC = AB + BC (Pythagoras property) D
2
2
BC = AC − AB 2 C
2
= 17 − 8 2
17 m
= 289 − 64 = 225
2
2
BC = 15 ⇒ BC = 15. So, BC = 15 m
Thus, the ladder reaches to a height of 15 m up the wall. A 8 m B
Example 15: Find the length of the diagonal of a rectangle whose length is 12 m and breadth is 9 m.
Solution: Let ABCD be the rectangle such as AB = 12 m, AD = 9 m and BD be the diagonal.
In DBAD,
2
2
2
BD = AD + AB (Pythagoras property)
= 9 + 12 2 D C
2
= 81 + 144 = 225
2
2
BD = 15 ⇒ BD = 15 m 9 m
Thus, the length of the diagonal BD is 15 m.
A 12 m B
Example 16: Two poles of 10 m and 22 m stand upright on a plane ground. If the distance between
the tops is 13 m, find the distance between their feet. A

Solution: Height of tower AB = 22 m
Height of tower CD = 10 m 13 m
CD = BE = 10 m C E 22 m
AE = AB – BE 10 m
AE = 22 m – 10 m = 12 m
In DACE, right angled at E. D B
2
2
AC = AE + CE (Pythagoras property)
2
2
CE = AC − AE
2
2
2
= 13 − 12 2
= 169 − 144 = 25
CE = 25 = 5 2
2
\ CE = 5 m
Hence, the distance between their feet is 5 m.

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