Let the lengths of the sides of the rectangle be x and y. Then A(Area) = xy and 2(x+y)=300. You can use substitution to make one equation that gives A in terms of either x or y instead of both.
2(x+y) = 300
x+y = 150
y = 150-x
A=x(150-x) <--(substitution)
The resulting equation is a quadratic equation that is concave down, so it has an absolute maximum. The x value of this maximum is going to be halfway between the zeroes of the function. The zeroes of the function can be found by setting A equal to 0:
0=x(150-x)
x=0, 150
So halfway between the zeroes is 75. Plug this into the quadratic equation to find the maximum area.
A=75(150-75)
A=75*75
A=5625
So the maximum area that can be enclosed is 5625 square feet.
Answer:
The approximate volume of the tank is 
Step-by-step explanation:
we know that
The volume of a hemisphere (water storage tank) is equal to
we have
assume
substitute
The ratio of the length of each side of the triangle to that of the hexagon is
<h3>What is equilateral triangle?</h3>
The triangle which has all the three sides equal in dimension is called the equilateral triangle.
According to the question,
Area of triangle = Area of rhombus = Area of hexagon
1/2 base x height = 1/2 diagonal1 xdiagonal2 = (3√3 / 2) side²
The triangle has equal base and height = a.
The hexagon has each side measuring b.
1/2 a² = (3√3 / 2) b²
Ratio of sides of triangle and hexagon is
a²/b² = 3√3
a/b = √ 5.19615
a/b = 2.2795
Thus, the ratio of each side of the triangle to that of the hexagon is 2.2795.
Learn more about equilateral triangle.
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Answer:
70.60
Step-by-step explanation:
