Question
The longer leg of a triangle is one foot less than twice the shorter leg. The hypotenuse is 17 feet long. Find the area of the triangle.
Answers
Reiny
short leg --- x
longer leg --- 2x-1
x^2 + (2x-1)^2 = 17^2
x^2 + 4x^2 - 4x + 1 = 289
5x^2 - 4x - 288 = 0
(x-8)(5x + 36) = 0
x = 8 or x is an inadmissable negative number
short leg = 8 ft
long leg = 15 ft
area = (1/2)(8)(15) = 60 ft^2
longer leg --- 2x-1
x^2 + (2x-1)^2 = 17^2
x^2 + 4x^2 - 4x + 1 = 289
5x^2 - 4x - 288 = 0
(x-8)(5x + 36) = 0
x = 8 or x is an inadmissable negative number
short leg = 8 ft
long leg = 15 ft
area = (1/2)(8)(15) = 60 ft^2