The shortest leg of a triangle is 4 feet shorter than the other leg. the hypotenuse of this triangle is 20 feet. what are the lengths of the two legs of this triangle?
Given: for example, a and b are the leg of the triangle a = b - 4 h = 20 ft
Solution: Use pythagoras theorem to find the solution a² + b² = h² (b - 4)² + b² = 20² b² - 8b + 16 + b² = 400 2b² - 8b +16 - 400 = 0 2b² - 8b - 384 = 0 -------------------------- (each side divided by 2) b² - 4b - 192 = 0 (b - 16)(b + 12) = 0 b = 16 or b = -12 The length of side can't be negative, so the value of b is 16
Subtitute the value of b to the equation to find a a = b - 4 a = 16 - 4 a = 12
