Question

The Hypotenuse of a right triangle is 6m more than twice the shortest side. If the third side is 2m less than teh Hypotenuse ,then find the Hypotenuse of a triangle ​

Answer 1

Answer:

26m

Step-by-step explanation:

Let the length of the shortest side be xx meters.

Then, hypotenuse=(2x+6)=(2x+6) metres

And the third side (2x+6-2)(2x+6−2) metre=(2x+4)=(2x+4) metres

By Pythagoras theorem, we have

{ (2x+6) }^{ 2 }={ x }^{ 2 }+{ (2x+4) }^{ 2 }(2x+6)  

2

=x  

2

+(2x+4)  

2

 

\Rightarrow { x }^{ 2 }-8x-20=0⇒x  

2

−8x−20=0

\Rightarrow { x }^{ 2 }-10x-2x-20=0⇒x  

2

−10x−2x−20=0

\Rightarrow (x-10)(x+2)=0⇒(x−10)(x+2)=0

\Rightarrow x=10\quad or\quad x=-2⇒x=10orx=−2

\because∵ xx can not be a negative $$\therefore  

\Rightarrow x=10⇒x=10

Length of the shortest side =10=10 metres

Length of the hypotenuse =(2x+6)=(2x+6) metres=26=26 metres

Length of the third side =(2x+4)=(2x+4) metres=24=24 metres

Hence the sides of the triangle are 10m,26m24m,

and obviously the longest side is the hypotenuse