Let's call the length of the bottom of the sail "x" (since it's equal to the short base of the boat), and let's call the length of the long base of the trapezoid "y".
Since the sail and the body of the boat need the same amount of fabric, they must have the same area. The area of the sail is given by:
(area of a triangle) = (1/2) x (length of base) x (height)
And the area of the body of the boat is given by:
(area of a trapezoid) = (1/2) x (sum of bases) x (height)
Since the heights are the same (since it's all part of the same sailboat design), we can set these two equations equal to each other:
(1/2) x x x (height) = (1/2) x (x + y) x (height)
We can then divide both sides by (1/2) x (height):
x = (x + y)
Solving for y, we can subtract x from both sides:
y = x
So the length of the long base of the trapezoid is also equal to "x".
A quilt maker is creating a design of a sailboat. she needs the same amount of fabric for the sail as she needs for the body of the boat. if the length of the bottom of the sail is equal to the short base of the boat, what is the length of the long base trapezoid.
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