A seamstress is designing a triangular flag so that the length of the base of the triangle, in inches, is 7 less than twice the height h. Express the area of the flag as a function of the height.
So am i just doing h(2h-7)/2?
b = 2h-7
A = 1/2 bh = h(2h-7)/2
Well, well, well, it looks like we have a flag in the making! Now, let's get down to business. We have a triangular flag, and the base of the triangle is 7 less than twice the height h. So, we can write the length of the base as 2h - 7.
Now, to find the area of a triangle, we can use the formula: A = (1/2) * base * height. In this case, the base is 2h - 7 and the height is h.
So, the area of the flag can be expressed as a function of the height h:
A(h) = (1/2) * (2h - 7) * h
And voilà! We've got ourselves a function that'll calculate the area of the flag based on the height. Happy sewing!
To express the area of the flag as a function of the height, we need to find the formula for the area of a triangle.
The area of a triangle is given by the formula: Area = (base * height) / 2.
Given that the length of the base of the triangle is 7 less than twice the height h, we can express it as (2h - 7).
Substituting the base and height in the formula, we get:
Area = ((2h - 7) * h) / 2
Simplifying the expression further, we have:
Area = (2h^2 - 7h) / 2
Therefore, the area of the flag can be expressed as a function of the height (h) using the formula: Area = (2h^2 - 7h) / 2.
To find the area of a triangular flag, we need to know the formula for the area of a triangle. The formula for the area of a triangle is given by:
Area = (1/2) * base * height
In this case, the base of the triangle is given as "7 less than twice the height h". So, we can express the base as (2h - 7). The height of the flag is given as 'h'.
Now, we can substitute the values into the formula for the area of the flag:
Area = (1/2) * base * height
Area = (1/2) * (2h - 7) * h
Simplifying further:
Area = (h*(2h - 7))/2
So, the area of the flag can be expressed as a function of the height 'h' as Area = (h*(2h - 7))/2.