MATH SOLVE

3 months ago

Q:
# 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.

Accepted Solution

A:

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

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