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PilotLPTM [1.2K]
3 years ago
6

NEED HELP NOW WILL GIVE BRAINLEIST!!!!!!b) Calculate the area of the red triangle to find the area of the garden. Show your work

. (2 points)

Mathematics
2 answers:
Arisa [49]3 years ago
6 0

Answer:

Area = 1/2ab sinc

Step-by-step explanation:

the area is given by two sides subtending an angle directly opposite a third side

diamong [38]3 years ago
5 0

Answer:  9 ab is the area of the garden.

No scale or dimensions are given, so

<u><em>Estimating to get a practical, reasonable answer:</em></u>

Using typical walkway widths to 6 ft, it is reasonable to calculate the <u>area the red triangle to be 486 square feet</u>

and the <u>area of the garden to be about 4400 square feet,</u> rounding up.

OR

Using a metric standard of 2 meters, The area of the red triangle would be 54m²

The area of the garden would be about 500m²

Step-by-step explanation:

The area of the red triangle is A = \frac{ab}{2}  That is assuming that it is a right triangle and side a is the altitude or height of the triangle and side b is the base.  

The measurements of the triangle are approximately in the proportion of 3, 4, 5, a typical "Pythagorean Triple" right triangle.

Estimating from rough measurements of the triangle and the dimensions of the garden as shown, it appears that the area of the garden is about 18 times the area of the red triangle.

The area of the triangle is half the area of a rectangle with the same side lengths a & b, so 9 ab is a good estimate of the area of the garden.

<u><em>If</em></u><em>  the walkways are the typical 6 foot width found in many public gardens, and </em> the length side b is the about 6 of those widths, and side a is about 4.5 of those widths, we can estimate the altitude to be 27 and the base to be 36 (in the proportion 3:4).

Area of the triangle estimate: A = 36ft × 27ft /2 = 486 square feet

<u>OR</u>

Using a metric standard, estimate  a 2 meter wide sidewalk, the area of the triangle can be reasonably calculated to be A = 9m × 12m /2 = 54 m²

The area of the garden would be 9 × 54 = 486m² rounded reasonably to 500m²

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a farmer has 100m for fence avaibiable, with which he intends to build a pen for his sheep. he intends to create a rectangular p
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The perimeter of the area of the pen the farmer intends to build for his

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Response:

i) The length and width of the rectangular pen are; <em>x</em>, and \dfrac{100 - x}{2}, therefore;

  • The area is; A = \dfrac{1}{2} \cdot x \cdot (100 - x)

ii) \hspace{0.5 cm}\dfrac{dA}{dx}  = 50 - x

\dfrac{d^2A}{dx^2} =  -1

iii) The value of <em>x</em> that makes the area as large as possible is x = 50

<h3>How is the function for the area and the maximum area obtained?</h3>

Given:

The length of fencing the farmer has = 100 m

Part of the area of the pen is a permanent stone wall.

Let <em>x</em> represent the length of the stone wall, we have;

2 × Width = 100 m - x

Therefore;

Width, <em>w</em>, of the rectangular pen, w = \mathbf{\dfrac{100 - x}{2}}

Area of a rectangle = Length × Width

Area of the rectangular pen, is therefore;

  • A = x \times \dfrac{100 - x}{2} = \underline{\dfrac{1}{2} \cdot x \cdot (100 - x)}

ii) \hspace{0.5 cm} \mathbf{\dfrac{dA}{dx}}, and \mathbf{\dfrac{d^2A}{dx^2} } are found as follows;

\dfrac{dA}{dx} = \mathbf{\dfrac{d}{dx} \left(  \dfrac{1}{2} \cdot x \cdot (100 - x) \right)} = \underline{50 - x}

\dfrac{d^2A}{dx^2} = \mathbf{ \dfrac{d}{dx} \left( 50 - x\right)} = \underline{-1}

iii) The value of <em>x</em> that makes the area as large as possible is given as follows;

Given that the second derivative, \dfrac{d^2A}{dx^2} =-1, is negative, we have;

At the maximum area, \dfrac{dA}{dx} = \mathbf{0}, which gives;

\dfrac{dA}{dx} = 50 - x = 0

x = 50

  • The value of x that makes the area as large as possible is <em>x</em>  =<u> 50</u>

Learn more about the maximum value of a function here:

brainly.com/question/19021959

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