Question

The hypotenuse of a right angle triangle exceeds one side by 1cm and the other by 18 cm find the sides

Answer 1

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.

:)