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Maurinko [17]
3 years ago
5

The length and width of a rectangle are consecutive odd integers. The perimeter is 120 meters. Find the length and width

Mathematics
1 answer:
poizon [28]3 years ago
3 0

Step-by-step explanation: Since the width and length are consecutive odd integers, call the width <em>x</em> and the length <em>x + 2</em>.

Now, it would be helpful to draw a picture of your rectangle

and label its parts to help you set up the equation.

Since the perimeter of the rectangle is 120 meters,

<em>x + x + (x + 2) + (x + 2) = 120</em>.

Simplifying from here we get 4x + 4 = 120.

Now subtract 4 from both sides to get 4x = 116.

Now divide both sides by 4 to get x = 29.

So the width of our rectangle is 29 meters

and the length, <em>x + 2</em>, is 31 meters,

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2 years ago
A clothing manufacturer uses the model a=f+4−−−−√−36−f−−−−−√ to estimate the amount of fabric to order from a mill. In the formu
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Questions:

A clothing manufacturer uses the model a = √(f + 4) - √(36 - f) to estimate the amount of fabric to order from a mill. In the formula, a is the number of apparel items (in hundreds) and f is the number of units of fabric needed. If 400 apparel items will be manufactured , how many units of fabric should be ordered?

Answer:

32 units of fabrics

Step-by-step explanation:

Given

a = \sqrt{f + 4} - \sqrt{36 - f}

Required

Find f when a  = 4

Substitute 4 for a

4 = \sqrt{f + 4} - \sqrt{36 - f}

Rewrite as:

\sqrt{36 - f} + 4 = \sqrt{f + 4}

Square both sides

(\sqrt{36 - f} + 4)^2 = (\sqrt{f + 4})^2

(\sqrt{36 - f} + 4)^2 = f + 4

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Collect Like Terms

8\sqrt{36 - f}= f +f+ 4 - 36 -16

8\sqrt{36 - f}= 2f -48

Divide through by 2

4\sqrt{36 - f}= f -24

Square both sides

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576-16f = f^2 - 48f + 576

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Collect like terms

f^2 - 48f + 16f = 0

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Factorize

f(f - 32) = 0

f = 0 or f = 32

f can not be 0 because some units must be ordered.

So, f = 32

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Answer:

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