Respuesta :
Answer: Shorter side = 10 feet
Longer side = 24 feet
Hypotenuse = 26 feet
The side lengths of the triangle are 10ft, 24ft and 26ft.
Step-by-step explanation:
Let the length of the shorter leg be x.
The length of the longer leg of a right triangle is 4ft more than twice the length of the shorter leg. This will be: = 2x + 4
The length of the hypotenuse is 6ft more than twice the length of the shorter leg. This will be: = 2x + 6
Note that the square of the hypothenuse will be equal to the square of the other two sides. This will be:
x² + (2x + 4)² = (2x + 6)²
x² + (2x + 4)(2x + 4) = (2x + 6)(2x + 6)
x² + 4x² + 8x + 8x + 16 = 4x² + 12x + 12x + 36
x² + 4x² + 16x + 16 = 4x² + 24x + 36
5x² + 16x + 16 = 4x² + 24x + 36
Collect like terms
5x² - 4x² + 16x - 24x + 16 - 36 = 0
x² - 8x - 20 = 0
x² - 10x + 2x - 20 = 0
x(x - 10) + 2(x - 10) = 0
Therefore, x - 10 = 0
x = 10
a. length of the shorter side = 10ft
b. Length of the longer side = 2x + 4 = 2(10) + 4 = 20 + 4 = 24ft
c. length of the hypotenuse = 2x + 6 = 2(10) + 6 = 20 + 6 = 26ft
d. The side lengths of the triangle are 10ft, 24ft and 26ft.
