Yes it is the last choice. You are correct
Answer:
Step-by-step explanation:
We have the equations
4x + 3y = 18 where x = the side of the square and y = the side of the triangle
For the areas:
A = x^2 + √3y/2* y/2
A = x^2 + √3y^2/4
From the first equation x = (18 - 3y)/4
So substituting in the area equation:
A = [ (18 - 3y)/4]^2 + √3y^2/4
A = (18 - 3y)^2 / 16 + √3y^2/4
Now for maximum / minimum area the derivative = 0 so we have
A' = 1/16 * 2(18 - 3y) * -3 + 1/4 * 2√3 y = 0
-3/8 (18 - 3y) + √3 y /2 = 0
-27/4 + 9y/8 + √3y /2 = 0
-54 + 9y + 4√3y = 0
y = 54 / 15.93
= 3.39 metres
So x = (18-3(3.39) / 4 = 1.96.
This is a minimum value for x.
So the total length of wire the square for minimum total area is 4 * 1.96
= 7.84 m
There is no maximum area as the equation for the total area is a quadratic with a positive leading coefficient.
The answer is A
A Parallelogram is a shape with 4 sides that has two pairs of parallel sides. The opposite sides must have equal length. This is accurate for this shape.
A Rectangle is a shape with 4 sides that has four right angles. This is accurate for this shape.
A rhombus is a shape with 4 sides of equal length. This is not accurate for this shape.
A square is a shape with 4 sides of equal length and four right angles. This is not accurate for this shape.
72*12 = 2*2*2*2*2*3*3*3 = 2^5*3^3
I believe the answer is B.
