The hypotenuse of a right triangle is 13ft long. The shorter leg is 7ft shorter than the longer leg. Find the side lengths of the triangle.
Mathematics · College · Wed Jan 13 2021
Answered on
Given:
Hypotenuse = 13 ft
Shorter leg is 7ft shorter than the longer leg,
So, let the shorter leg be x ft
Then, longer leg is x + 7 ft
By phythogoras theorem
H² = B² + P²
13² = x² + (x +7)²
169 = x² + x² + 14x + 49
2x² + 14x + 49 - 169 = 0
2x² + 14x -120 = 0
Or, x² + 7x - 60 = 0
By middle-term split method
x² + 12x - 5x - 60 =0
x(x + 12) - 5(x +12) = 0
(x + 12) (x -5) =0
Let x + 12 = 0
x = -12
Length cannot be in negative
x - 5 = 0
x = 5
So, shorter leg = 5 ft
Longer leg = 5 + 7 = 12 ft