Answer: 43.5
Step-by-step explanation:
Answer:
Step-by-step explanation:
Suppose that the side length is s. Imagine that one side is level. Draw a vertical line through the top vertex perpendicular to the base (level side). Label this vertical line "h." Then h and s are related as follows:
√3 h
sin 60 degrees = ------- = --------
2 s
s√3
and so h = the height of the triangle = -----------
2
The area of this triangle is (1/2)(base)(height), which here is:
(1/2)(s/2)( s√3 /2), or
(s^2)√3
A = ---------------
8
Solve either equation for either variable. Since the second one has y on its own, the easiest choice is to solve that for y.
-5x + y = 13 ⇒ y = 5x + 13
Now substitute this into the other equation to eliminate y and rewrite it entirely in terms of x :
-3x + 3y = 3 ⇒ -3x + 3 (5x + 13) = 3
Simplify and solve for x :
-3x + 15x + 39 = 3
12x = -36
x = -3
Substitute this into either original equation to solve for y. Plugging x = -3 into the first equation would give
-3 (-3) + 3y = 3
9 + 3y = 3
3y = -6
y = -2
So the solution to the system of equations is (x, y) = (-3, -2).
