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AnnZ [28]
3 years ago
5

Kat is painting the edge of a triangular stage prop with reflective orange paint. The lengths of the edges of the triangle are (

3x – 4) feet, (x^2 – 1) feet, and (2x^2 – 15) feet. What is the perimeter of the triangle given the value of x = 4?
Mathematics
1 answer:
vfiekz [6]3 years ago
4 0
We are given with three lengths of a triangle expressed in terms and variables: (3x – 4) feet, (x^2 – 1) feet,  and (2x^2 – 15) feet. The perimeter of the triangle is equal to the sum of the three sides of the triangle. In this case, the sum is 3x^2 + 3x -20. When x is equal to 4, we substitute  <span>3*16 + 3*4 -20 equal to 40 feet.</span>
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2 years ago
A farmer has 520 feet of fencing to construct a rectangular pen up against the straight side of a barn, using the barn for one s
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Answer:

310\text{ feet and }210\text{ feet}

Step-by-step explanation:

GIVEN: A farmer has 520 \text{ feet} of fencing to construct a rectangular pen up against the straight side of a barn, using the barn for one side of the pen. The length of the barn is 310 \text{ feet}.

TO FIND: Determine the dimensions of the rectangle of maximum area that can be enclosed under these conditions.

SOLUTION:

Let the length of rectangle be x and y

perimeter of rectangular pen =2(x+y)=520\text{ feet}

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                                               y=260-x

area of rectangular pen =\text{length}\times\text{width}

                                       =xy

putting value of y

=x(260-x)

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to maximize \frac{d \text{(area)}}{dx}=0

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but the dimensions must be lesser or equal to than that of barn.

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                              width of rectangular pen =210\text{ feet}

Maximum area of rectangular pen =310\times210=65100\text{ feet}^2

Hence maximum area of rectangular pen is 65100\text{ feet}^2 and dimensions are 310\text{ feet and }210\text{ feet}

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