The longer leg of a right triangle is one foot less than twice the shorter leg. The hypotenuse of the triangle is 17 feet long. What is the area of the triangle?
Given that the longer leg of the right triangle is one foot less than twice the shorter leg, we can set up an equation that will help find the length of the shorter and longer leg.
a = x ft
b = 2x - 1 ft
c = 17 ft
Using the pythagorean theorem, a2 + b2 = c2, you can find the length of both the shorter and longer leg.
a2 + b2 = c2
x2 + (2x -1)2 = 172
x2 + 2x2 + 1 = 289
3x2 / 3 = 288 / 3
x2 = 96
sqrt(x2) = sqrt(96)
x = 9.8
The length of the shorter leg is 9.8 ft.
To find the length of the longer leg, substitute 9.8 for x in 2x - 1.
2(9.8) - 1 =
19.6 - 1
The length of the longer leg is 18.6 ft.
To find the area of a triangle, multiply the base by the height, and then divide by 2.
area = ( 9.8 x 18.6 ) / 2
area = 182.28 / 2
area = 91.12 ft
The area of the triangle is 91.12 ft.