What is the area of this figure?
1 answer:
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Answer:
Therefore the length and width of the playground are 15.5 feet and 12.9 feet respectively.
Step-by-step explanation:
Given that, a homeowner plans to enclose a 200 square foot rectangle playground.
Let the width of the playground be y and the length of the playground be x which is the side along the boundary.
The perimeter of the playground is = 2(length +width)
=2(x+y) foot
The material costs $1 per foot.
Therefore total cost to give boundary of the play ground
=$[ 2(x+y)×1]
=$[2(x+y)]
But the neighbor will play one third of the side x foot.
So the neighbor will play
Now homeowner's total cost for the material is
where C(x) is total cost of material in $.
Given that the area of the playground is 200.
We know that,
The area of a rectangle is =length×width
=xy square foot
∴xy=200
Putting the value of y in C(x)
The domain of C is.
Differentiating with respect to x
Again differentiating with respect to x
To find the critical point set C'(x)=0
Therefore
Therefore at x= 15.5 , C(x) is minimum.
Putting the value of x in we get
=12.9
Therefore the length and width of the playground are 15.5 feet and 12.9 feet respectively.
The volume of the given right triangular prism can be found by first calculating the area of the right triangle and then multiplying it with the length of the prism.
Let us find the area of the right triangle. As can be seen from the diagram the height, h of the right triangle is 7 cm and the base, b of the right triangle is 4 cm.
Therefore, the area of the triangle is:
Area=
Thus, the volume of the right triangular prism will be:
Volume=Area x Length of the prism
Volume=
Thus, out of the given options, option A is the correct option.