Question

The flower garden has the shape of a right triangle. 51 ft of a perennial border forms the hypotenuse of the​ triangle, and one leg is 21 ft longer than other leg. find the lengths of the legs. a right triangle has a vertical side of unlabeled length, a horizontal side of length x, and a hypotenuse of length 51 feet.

Answer 1

Let
x------> larger leg
y------> smaller leg

we now that
x=y+21----> equation 1
51²=x²+y²----> equation 2
substitute 1 in 2

2601=[y+21]²+y²----> 2601=y²+42y+441+y²
2y²+42y-2160=0

using a graph tool----> to resolve the second order equation
see the attached figure

the solution is
y=24 ft
x=y+21-----> x=24+21-----> x=45 ft

the answer is
The length of the larger leg is 45 f
The length of the smaller leg is 24 ft