Question

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

Answer 1

let abc be the right triangle.right angled at b &ab be the shortest side .
let ab=3x and ac=4x
by pythagoras theorem,
ab^2+bc^2=ac^2
(3x)^2+(4x)^2=ac^2=9x^2+16x^2=25x^2
ac=5x.
let aced be the rectangle.
ac=ed & ec=ad
breadth of the rectangle=4/5*length=4/5*5x=4x
perimeter=ac+ec+ed+ad=5x+4x+5x+4x=18x=180 cm
therefore,x=180/18=10
shortest side =3x=3*10=30 cm
please mark my answer as brainliest if i am correct.
hope it helps..........and feel free to ask if u have any doubt in this sum