Question

The hypotenuse of a right triangle is 5 metres. If the smaller leg is doubled and the longer leg is tripled, then new hypotenuse is 6root 5 metres. Find the sides of the triangle.

Answer 1

ANSWER

Length of hypotensue=3  

10

​  

 

According to pythagoras theorem,

x  

2

+y  

2

=(3  

10

​  

)  

2

=90

⇒x  

2

+y  

2

=90......(1)

The smaller side is tripled =3x

The larger side is doubled =2y

New hypotenuse=9  

5

​  

 

Now,

(3x)  

2

+(2y)  

2

=(9  

5

​  

)  

2

 

⇒9x  

2

+4y  

2

=405

⇒5x  

2

+4x  

2

+4y  

2

=405

⇒5x  

2

+4(x  

2

+y  

2

)=405

⇒5x  

2

+4×90=405

⇒5x  

2

=405−360

⇒x  

2

=  

5

45

​  

 

⇒x  

2

=9

⇒x=3

Put x=3 in (1) and we get,

y=9

Hence, this is the answer.