The hypotenuse of a right angle triangle exceeds one side by 1cm and the other by 18 cm find the sides
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Hi ,
Let a , b and c are three sides of the right
angled Triangle .
c is the hypotenuse .
according to the problem given ,
a = c - 1
b = c - 18
By Pythagoras theorem
a² + b² = c²
( c - 1 )² + ( c - 18 )² = c²
c² - 2c + 1 + c² - 36c + 324 = c²
c² - 38c + 325 = 0
c² -13c - 25c + 325 = 0
c ( c - 13 ) - 25 ( c - 13 ) = 0
( c - 13 ) ( c - 25 ) = 0
c - 13 = 0 or c - 25 = 0
c = 13 or c = 25
Therefore ,
Required 3 sides are ,
1 ) if c = 13 ,
a = c - 1 = 13 - 1 = 12 ,
b = c - 18 = 13 - 18 = -5
it is not possible .
2 ) if c = 25 ,
a = c - 1 = 25 - 1 = 24 ,
b = c - 18 = 25 - 18 = 7
Therefore ,
3 sides are 24 , 7 and hypotenuse = 25cm
I hope this helps you.
:)
Let a , b and c are three sides of the right
angled Triangle .
c is the hypotenuse .
according to the problem given ,
a = c - 1
b = c - 18
By Pythagoras theorem
a² + b² = c²
( c - 1 )² + ( c - 18 )² = c²
c² - 2c + 1 + c² - 36c + 324 = c²
c² - 38c + 325 = 0
c² -13c - 25c + 325 = 0
c ( c - 13 ) - 25 ( c - 13 ) = 0
( c - 13 ) ( c - 25 ) = 0
c - 13 = 0 or c - 25 = 0
c = 13 or c = 25
Therefore ,
Required 3 sides are ,
1 ) if c = 13 ,
a = c - 1 = 13 - 1 = 12 ,
b = c - 18 = 13 - 18 = -5
it is not possible .
2 ) if c = 25 ,
a = c - 1 = 25 - 1 = 24 ,
b = c - 18 = 25 - 18 = 7
Therefore ,
3 sides are 24 , 7 and hypotenuse = 25cm
I hope this helps you.
:)
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