Question

the sides other than hypotenuse of a right triangle are in the ratio 3 ratio for a rectangle is described always hypotenuse the hypotenuse is the longest side of the rectangle the breadth of the rectangle is four fifth of its length find the shortest side of the right triangle if the perimeter of the rectangle is 180 cm

Answer 1

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