Let's find the area of the base.
It's a rectangle that's 3.8 by 4.8, so let's multiply.
3.8×4.8=18.24
We have two different triangles.
Triangle one has a height of 2.6 and base of 4.8. But there are two of them.
2.6×4.8×0.5=6.24×2= 12.48; this is the area of two triangles.
Another set of triangles has a height of 2.9 and a base of 3.8.
2.9×3.8×0.5=5.51×2=11.02
Let's add all the areas together.
18.24+12.48+11.02
41.74
The surface area is 41.74 m², so the third option.
Let
x---------> the length side of the rectangular area
y---------> the width side of the rectangular area
we know that
the area of the rectangle is equal to
-----> equation
The perimeter of the rectangle is equal to
but remember that the fourth side of the rectangle will be formed by a portion of the barn wall
so
-----> equation
<em>To minimize the cost we must minimize the perimeter</em>
Substitute the equation in the equation
Using a graph tool
see the attached figure
The minimum of the graph is the point
that means for
the perimeter is a minimum and equal to
<u>Find the value of y</u>
The cost of fencing is equal to
therefore
<u>the answer is</u>
the length side of the the fourth wall will be
<span>Setting expressions equal to one another gives us an equation.
In an equation, our goal is to isolate the variable; we must "undo" everything that has been done to the variable. We work backward; the last thing done to the variable will be the first thing we undo.
We "undo" things by performing the opposite operation; for instance, if the last thing done to our variable was that 3 was subtracted from it, we would undo that first by adding 3 to both sides.
What we do to one side we must do to the other in order to preserve equality.
We would continue this process of working backward until the variable was isolated; this would give us our solution.</span>