A city lot has the shape of a right triangle whose hypotenus

A city lot has the shape of a right triangle whose hypotenuse is 3 ft longer than one of the other sides. The perimeter of the lot is 396 ft. How long is each side of the lot?

Solution

let 2 sides of right triangle be x , y and hypotenuse be h

given hypotenuse is 3 ft longer than one of the other sides

=> h =3+x

given The perimeter of the lot is 396 ft

x+y+h =396

x+y+3+x=396

2x+y=393

=>y=393-2x

by pythogorus theorem in right triangle

x²+y²=h²

x²+(393-2x)²=(3+x)²

x²+154449-1572x+4x²=9+6x+x²

154440-1578x+4x²=0

4x²-1578x+154440=0

x=[1578+(1578² -4*4*154440)]/(2*4) ,x=[1578-(1578² -4*4*154440)]/(2*4)

x=214.5, x =180

but x cannot be 214.5 as y =393- 2*214.5=-36<0

x =180

y=393-2*180 =33

h =3+180=183

short side =33ft

other side = 180ft

longer side =183ft