Question

the sides (other than hypotenuse )of a right triangle are in the ratio 3:4, A rectangle is described on its hypotenuse ,the hyptenuse being the longer side of the rectangle . the breadth of the rectangle is 4/5 of its length. Find the shortest side of the triangle if the perimeter of the rectangle is 180cm.

Answer 1

the shortest side of triangle is 30cm

Answer 2

Here is your solution

Given :-

Given  :-
The sides (other than hypotenuse) of a right angled triangle are in the ratio 3 : 4.

Let ratio coefficient  =  x 

So,

Sides  =  3x  and 4x

We know :-

Hypotenuse ^2 =  Adjacent^ 2 + Opposite ^2

Hypotenuse^ 2 =  ( 3x )2 + ( 4x )2

Hypotenuse ^2 =  9x ^2 + 16 x ^2

Hypotenuse ^2 =  25 x ^2

Hypotenuse ^2 =  ( 5x )^ 2

Hypotenuse =   5x  

As given : The hypotenuse being the longer side of the rectangle. The breadth of the rectangle in four-fifth of its length.
So,

Length of rectangle  = 5 x

And

Breadth  = 4x 

We know perimeter of rectangle  =  2 ( Length  + Breadth )

Given : The perimeter of the rectangle is 180 cm , So

2 ( 5x  + 4x ) =  180

2 ( 9x ) =  180

18 x  =  180

x  =  10 

So,

Sides of triangle  =  3 ( 10 ) =  30 cm , 4 ( 10 ) = 40 cm and  Hypotenuse 5 ( 10 ) =  50 cm

Shortest side of right angle triangle  =  30 cm                                                  
hope it helps you