A sailboat has a triangular sail with an area of 20 square feet. The height of the sail is 6 feet more than the length of the base of the sail. Find the height of the sail.
. .area of triangle = 1/2 bh . Height of sail . = 6+b. . .20 = 1/2 x b x (6 + b) . 20= 1/2 x 6b + b^2. 6b +b^2 =40. . b^2 + 6b - 40. . (b+10)(b - 4). b=-10 or 4 and h =6 + b . Height of sail =6 +4 =10. . Height of sail =10 meters
Going against the wind, a cyclist was able to reach 60 km in a matter of 4 hours. With the wind, she was able to cover 150 km in 6 hours. What would be the speed of the cyclist in calm air and how fast was the wind blowing?
Answer:
The wind was blowing at ____ kph.
To find the height of the sail, we can set up an equation using the given information.
Let's assume the length of the base of the sail is 'x' feet.
According to the given information, the height of the sail is 6 feet more than the length of the base.
So, the height of the sail is x + 6 feet.
Now, we can use the formula for the area of a triangle to solve for the height.
The area of a triangle is given by the formula:
Area = (1/2) * base * height
Given that the area of the sail is 20 square feet and the base is 'x' feet, we can write the equation as:
20 = (1/2) * x * (x + 6)
To solve this equation, we need to simplify and solve for 'x'.
Multiplying both sides by 2:
40 = x * (x + 6)
Expanding the equation:
40 = x^2 + 6x
Rearranging the equation in quadratic form:
x^2 + 6x - 40 = 0
To solve this quadratic equation, we can factor it or use the quadratic formula.
By factoring or using the quadratic formula, we find that 'x' can be either -10 or 4.
Since the length cannot be negative, we discard the negative value and consider the positive value.
So, the length of the base of the sail is 4 feet.
Now, we can find the height by substituting the value of x into the equation:
Height = x + 6
Height = 4 + 6
Height = 10 feet
Therefore, the height of the sail is 10 feet.
base length --- x
height ---- x+6
(1/2)(x)(x+6) = 20
x(x+6) = 40
x^2 + 6x - 40 = 0
(x+10)(x-4) = 0
x = 4 or x is some negative
the height is 10 ft , (from x+6)