The area of a triangular sail (for a sailboat) is 30 meters squared. If the height of this triangular sail is two less than twice the length of the base, find the dimensions ( height and base ) of the triangular sail.
If the base is b, then
(1/2)bh = 30
(1/2)b(2b-2) = 30
...
To find the dimensions of the triangular sail, we need to set up an equation based on the given information.
Let's assume the height of the triangular sail is 'h' and the base length is 'b'.
We are given that the area of the triangular sail is 30 square meters. The formula for the area of a triangle is: Area = 0.5 * base * height.
So, we can write the equation as follows:
30 = 0.5 * b * h
We are also given that the height is two less than twice the length of the base, which can be written as:
h = 2b - 2
Now we can substitute this expression for 'h' in the previous equation:
30 = 0.5 * b * (2b - 2)
Now we can solve this equation for 'b':
30 = b * (b - 1)
30 = b^2 - b
Rearranging the equation, we have a quadratic equation:
b^2 - b - 30 = 0
Now we can factorize this quadratic equation to find the values of 'b':
(b - 6)(b + 5) = 0
So, we have two values for 'b': b = 6 and b = -5.
Since the base length cannot be negative, we can discard the solution b = -5.
Therefore, the base length of the triangular sail is 6 meters.
Now, substitute this value of 'b' back into the expression for 'h':
h = 2 * 6 - 2
h = 12 - 2
h = 10
So, the height of the triangular sail is 10 meters and the base length is 6 meters.