Question 1206702
the garden forms a right triangle.
the horizontal side is x
the vertical side is x + 5
the hypotenuse is 2x.


use pythagorus theorem to get x^2 + (x + 5)^2 = (2x)^2
simplify to get x^2 + x^2 + 10x + 25 = 4x^2
combine like terms and subtract the left side of the equation from both sides of the equation and flip sides to get:
4x^2 - 2x^2 - 10x - 25 = 0
simplify to get:
2x^2 - 10x - 25 = 0
factor this quadratic equation to get:
x = 6.8301270189222 or x = -1.8301270189222
x can't be negative, so x = 6.8301270189222.
the perimeter is equal to x + 2x + x + 5 = 32.32050808 feet.
divide that by 8 feet to get 4.040063509.
she will need 5 eight foot lengths of timber = 40 feet of timber.
at 32.88 for each 8 feet of timber, the cost will be 164.8 dollars.
she will have 40 minus 32.32050808 = 7.679491924 feet of timber left over.