Answer:
Option 4: 80 inches
Explanation:
We can find the length of the window's base using a system of equations, where:
- h is the window's height,
- and b is the window's base.
First equation:
We know that the formula for the area of a triangle is given by:
A = 1/2bh, where
- A is the area in units squared,
- b is the base,
- and h is the height.
Since we're told that the window's area is 800 in.^2, our first equation is given by:
800 = 1/2bh
Second equation:
Since we're told that the window's base if four times its height, our second equation is given by:
b = 4h
Method to solve: Substitution:
Solving for h:
The second equation in our system is already arranged in such a way that allows us to substitute it for b in the first equation (i.e., 800 = 1/2bh) to solve for h:
800 = 1/2bh
800 = 1/2(4h)(h)
800 = (2h)(h)
(800 = 2h^2) / 2
±√400 = √h
±20 = h
20 = h
- I wrote the "±" symbol since normally, there's two answers to a square root (2^2 = 4 and (-2)^2 = 4).
However, because we can't have a negative height, the height is simply 20 inches.
Solving for b:
Now we can solve for b by plugging in 20 for h in the second equation (i.e., b = 4h):
b = 4(20)
b = 80
Thus, the length of the base is 80 inches (Option 4).