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disa [49]
3 years ago
10

The area of a rectangle is (81x2 − 4y2) square units. Determine the dimensions of the rectangle by factoring the area expression

completely. Show your work. (5 points)
Mathematics
1 answer:
oksano4ka [1.4K]3 years ago
6 0

Answer:

The dimension of the rectangle are 9\cdot x - 2\cdot y units and 9\cdot x + 2\cdot y units, respectively.

Step-by-step explanation:

Geometrically speaking, the area of a rectangle is equal to the product of its base and its height. If we know that area of the figure is 81\cdot x^{2} - 4\cdot y^{2} square units, then we proceed to factor the expression:

1) A = 81\cdot x^{2} - 4\cdot y^{2} Given

2) A = (9\cdot x -2\cdot y)\cdot (9\cdot x + 2\cdot y) a^{2} - b^{2} = (a + b) \cdot (a - b)/Result

The dimension of the rectangle are 9\cdot x - 2\cdot y units and 9\cdot x + 2\cdot y units, respectively.

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Step-by-step explanation:

The Length ,

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Explanation:

Given:

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divide both sides by 2

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(

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transposing 4402 to the right side of the equation

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5

W

2

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13

W

−

4402

by quadratic formula

W

=

−

(

−

13

)

+

√

(

−

13

)

2

−

4

(

5

)

(

−

4402

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2

(

5

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W

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[

13

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169

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W

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+

(

√

88209

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10

W

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13

+

297

10

W

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10

W

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31

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W

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26

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10

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31

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26

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284

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answer

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−

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−

13

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−

√

−

(

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13

2

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4

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this is discarded since this will yield a negative

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