SOLUTION: The length of the base of the triangular sheet of canvas above the door of the tent shown below is 2 feet more than twice its height. The area is 56 square feet. Find the height an
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Question 1128434: The length of the base of the triangular sheet of canvas above the door of the tent shown below is 2 feet more than twice its height. The area is 56 square feet. Find the height and the length of the base of the triangle.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Since there is no diagram, I am going to assume:
:
The length of the base of the triangle is 2 feet more than twice its height.
b = 2h + 2
The area is 56 square feet.
b*h = 56
multiply by 2, get rid of the fraction
b * h = 112
Find the height and the length of the base of the triangle.
replace b with (2h+2) in the above equation
(2h+2)*h = 112
2h^2 + 2h = 112
A quadratic equation
2h^2 + 2h - 112 = 0
simplify, divide by 2
h^2 + h - 56 = 0
Factors to
(h+8)(h-7) = 0
the positive solution
h = 7 ft is the height
then
b = 2(7) + 2
b = 16 ft is the height
:
;
Check
16*7 = 56
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