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m_a_m_a [10]
2 years ago
6

Jim is enclosing a rectangular garden with 170 feet of fencing. The length of the garden is 10 feet more than twice it’s width,

w. Determine the area of the garden, in sqaure feet. Use an algebraic approach to model the problem.
Mathematics
1 answer:
Darina [25.2K]2 years ago
6 0

Answer:

1,500\ ft^2

Step-by-step explanation:

Let

L ----> the length of the rectangular garden in feet

w ---> the width of  the rectangular garden in feet

step 1

Find the width

we know that

The perimeter of the rectangular garden is

P=2(L+W)

P=170\ ft

so

170=2(L+W)

Simplify

85=(L+W) ----> equation A

L=2W+10 ----> equation B

substitute equation B in equation A and solve for W

85=(2W+10+W)

85-10=3W

3W=75

W=25\ ft

Find the value of L

L=2(25)+10=60\ ft

step 2

Find the area

we know that

The area of the rectangular garden is

A=(LW)

substitute the values

A=(60)(25)=1,500\ ft^2

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Straightforward use of the inverse tangent function of a calculator will tell you θ ≈ -0.08678 radians. This is an angle in the 4th quadrant, where your restriction on θ places it. (To comply with the restriction, you would need to consider the angle value to be 2π-0.08678 radians. The trig values for this angle are the same as the trig values for -0.08678 radians.)

Likewise, straightforward use of the calculator to find the other function values gives ...

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_____

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Depending on the mode setting of your calculator, the arctan or tan⁻¹ function may give you a value in degrees, not radians. That doesn't matter for this problem. sin(arctan(-0.087)) is the same whether the angle is degrees or radians, as long as you don't change the mode in the middle of the computation.

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<em>Alternate solution</em>

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This more complicated computation gives the same result as above.

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