1. ## Algebraic Reprsentation

An engineer measured the dimensions for a rectangular site by usinga wooden pole of unknown length x. The length of the rectangular siteis 2 pole measures increased by 3 feet, while the width is 1 pole measure decreased by 4 feet. Write an algebraic representation, in terms of x, for the perimeter of the site.

2. Hey there magentarita,

Since the perimeter of the site is rectangular, it is of the form:

$\displaystyle P = 2(\text {length } \times {\text { width}})$

From the question...

$\displaystyle P = 2((2x + 3) + (x - 4))$

$\displaystyle P = 2(3x - 1)$

$\displaystyle P = 6x - 2 \text{ feet}$

Alternately, the wording of the question could be seen as a little ambiguous for the following reasons...

"The length of the rectangular site is 2 pole measures increased by 3 feet...

Does this mean, instead, 2(x + 3)?

If this is the case, then the perimeter is:

$\displaystyle P = 2((2(x + 3)) + (x - 4))$

$\displaystyle P = 2((2x + 6) + (x - 4))$

$\displaystyle P = 2(3x - 2)$

$\displaystyle P = 6x - 4 \text { feet}$

In general math questions, however, I would favour the initial reading.

Trust this helps.

3. ## great

Originally Posted by MakeANote
Hey there magentarita,

Since the perimeter of the site is rectangular, it is of the form:

$\displaystyle P = 2(\text {length } \times {\text { width}})$

From the question...

$\displaystyle P = 2((2x + 3) + (x - 4))$

$\displaystyle P = 2(3x - 1)$

$\displaystyle P = 6x - 2 \text{ feet}$

Alternately, the wording of the question could be seen as a little ambiguous for the following reasons...

"The length of the rectangular site is 2 pole measures increased by 3 feet...

Does this mean, instead, 2(x + 3)?

If this is the case, then the perimeter is:

$\displaystyle P = 2((2(x + 3)) + (x - 4))$

$\displaystyle P = 2((2x + 6) + (x - 4))$

$\displaystyle P = 2(3x - 2)$

$\displaystyle P = 6x - 4 \text { feet}$

In general math questions, however, I would favour the initial reading.

Trust this helps.
Thank you for taking time out to help me.