Answer:
B) 
Step-by-step explanation:
to find the volume we need to find first the area of the triangle, and then multiply by 11 which is the length of the prism:
the measurements are:
the area of the triangle in one side is:
and now to find the volume of the prism we multiply the area of the triangle by the length of the prism:
which is option B)
More information is needed
Answer:
that is the solution is to the question
They are called identities because:
w-x = 0
w = x (carry x to the other side) is the same as x = w
in the other case:
wx-x = w / divide by w on both side
x -x = 0
x = x (carry x to the other side)
In both cases the equations are the same.
We know that the area of a rectangle is length * width, and the area of a triangle is 1/2 * base * height. However, we know that the areas are equal, or that
lw = 1/2bh
If we substitute in the measurements that we know, we can solve the following equation for x.
5x + 1 (x) = 1/2(8x)(x+1)
Let's simplify this equation by multiplying.
5x² + x = 4x² + 4x
Now, let's bring all of the variables to one side of the equation.
x² - 3x = 0
Finally, we should factor out the Greatest Common Factor.
x(x-3) = 0
Therefore, by the Zero Product Property, x = 0, 3. But since the measurement of the short side length of the rectangle is x, it cannot be zero. Thus, x = 3.
The question asks for the area of the rectangle, which is <span>5x² + x.
</span>
Let's solve this expression for x = 3.
5(3)² + 3
5(9) + 3
45 + 3
48
Therefore, the area of the rectangle is 48 square units, or option B.
