SOLUTION: The flower garden has the shape of a right triangle. 20ft of a perennial border forms the hypotenuse of the triangle, and one leg is 4ft longer than the other leg.Find the lengths

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The flower garden has the shape of a right triangle. 20ft of a perennial border forms the hypotenuse of the triangle, and one leg is 4ft longer than the other leg.Find the lengths       Log On


   

Question 162658: The flower garden has the shape of a right triangle. 20ft of a perennial border forms the hypotenuse of the triangle, and one leg is 4ft longer than the other leg.Find the lengths of the legs.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the length of the hypotenuse = c ft
Let the length of the shorter side = b ft
Let the length of the longer side = a ft
From the Pythagorean theorem,
c%5E2+=+a%5E2+%2B+b%5E2
c+=+20 ft
a+=+b+%2B+4ft
20%5E2+=+%28b+%2B+4%29%5E2+%2B+b%5E2
400+=+b%5E2+%2B+8b+%2B+16+%2B+b%5E2
2b%5E2+%2B+8b+-+384+=+0
b%5E2+%2B+4b+-+192+=+0
Complete the square by taking 1/2 of the coefficient of
b, square it, add it to both sides. First add 192 to
both sides
b%5E2+%2B+4b+=+192
b%5E2+%2B+4b+%2B+%284%2F2%29%5E2+=+192+%2B+%284%2F2%29%5E2
b%5E2+%2B+4b+%2B+4+=+192+%2B+4
%28b+%2B+2%29%5E2+=+196
Take the square root of both sides (there is a (-) square root also,
but I can ignore it)
b+%2B+2+=+14
b+=+12
a+=+b+%2B+4
a+=+16
The lengths of the legs are 12 ft and 16 ft
check answer:
c%5E2+=+a%5E2+%2B+b%5E2
20%5E2+=+16%5E2+%2B+12%5E2
400+=+256+%2B+144
400+=+400
OK