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Referring to the figure, the area and one dimension of a

rectangle are shown. Find the missing dimension.

Referring to the figure, the area and one dimension of a rectangle are shown. Find-example-1
User Alex Dn
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Answer:

2x -3

Explanation:

Given a rectangle with area 2x²+x-6 and one dimension x+2, you want the other dimension.

Area

The area of a rectangle is the product of its length and width. Given the area and the width, we can solve for the length:

A = LW

A/W = L

So, the missing dimension is the quotient of (2x²+x-6) and (x+2). In the attached, we find that quotient by synthetic division.

The missing dimension is 2x -3.

__

Additional comment

You can also use any of several methods to factor the area expression. We recognize that numbers of interest will be factors of (2)(-6) that total +1. Those would be -3 and +4. Then we can write ...

A = 2x² +x -6 = (2x -3)(2x +4)/2 = (2x -3)(x +2)

We recognize the factor (x+2) as the given dimension, so the missing dimension is (2x -3).

Referring to the figure, the area and one dimension of a rectangle are shown. Find-example-1
User Agostinho
by
8.8k points

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