SOLUTION: Haley is making a small garden in the shape of a right triangle. The garden will be framed using landscaping timbers. One side of the garden is 5 feet longer than the other and the

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Question 1206702: Haley is making a small garden in the shape of a right triangle. The garden will be framed using landscaping timbers. One side of the garden is 5 feet longer than the other and the longest side of the garden is twice as long as the short side. A hardware store exclusively sells landscaping timber in full 8-foot lengths for $32.88. Determine how much Haley will spend to build her garden and how much timber she will have left over for another project.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
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.