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3 years ago

A Rectangular has area 12a^2 and perimeter 14a what are the dimensions of this Rectangular?

Mathematics

1 answer:

Nataliya [291]3 years ago

5 0

9514 1404 393

Answer:

3a by 4a

Step-by-step explanation:

For dimensions L and W, the area and perimeter are ...

A = LW = 12a^2

P = 2(L+W) = 14a

Using the second equation, we can find L:

L +W = 7a . . . . . divide by 2

L = 7a -W

Substituting into the area formula gives the quadratic ...

(7a -W)(W) = 12a^2

W^2 -7aW +12a^2 = 0 . . . . arrange in standard form

(W -3a)(W -4a) = 0 . . . . . . . factor (find factors of 12 that total 7)

Then we have the two solutions ...

W = 3a, L = 4a

W = 4a, L = 3a

The rectangle dimensions are 3a by 4a.

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————————

You can actually use either the product rule or the chain rule for this one. Observe:

• Method I:

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Differentiate it by applying the product rule:

$\mathsf{\dfrac{dy}{dx}=\dfrac{d}{dx}(cos\,x\cdot cos\,x)}\\\\\\
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—————

• Method II:

You can also treat y as a composite function:

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and then, differentiate y by applying the chain rule:

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and then you get the same answer:

$\therefore~~\boxed{\begin{array}{c}\mathsf{\dfrac{dy}{dx}=-2\,sin\,x\cdot cos\,x}\end{array}}\qquad\quad\checkmark$

I hope this helps. =)

Tags: <em>derivative chain rule product rule composite function trigonometric trig squared cosine cos differential integral calculus</em>

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A Rectangular has area 12a^2 and perimeter 14a what are the dimensions of this Rectangular?​

A Rectangular has area 12a^2 and perimeter 14a what are the dimensions of this Rectangular?