Question

A garden has the shape of a right triangle with one leg 55 meters longer than the other. the hypotenuse is 55 meters less than twice the length of the shorter leg. what is the length of the shorter​ leg? the length of the shorter leg is nothing meters.

Answer 1

Let
x---------> longer leg
y--------> shorter leg

we know that
x=55+y
hypotenuse=2y-55

in a right triangle
c²=a²+b²
where 
c is the hypotenuse
a and b are the legs
so
hypotenuse²=x²+y²------> (2y-55)²=(55+y)²+y²
4y²-220y+3025=y²+110y+3025+y²
2y²-330y=0------> divided by 2-----> y²-165y=0

using a graph tool
see the attached figure
the solution is
y=165 m

the answer is
the length of the shorter​ leg is 165 m