A rectangular garden has a perimeter of 92 feet. If the length of the

A rectangular garden has a perimeter of $92$ feet. If the length of the garden is $1$ foot greater than twice its width, what is the length of the garden, in feet?

  1. $15$
  2. $23$
  3. $30$
  4. $31$
  5. $62$

So, you were trying to be a good test taker and practice for the GRE with PowerPrep online. Buuuut then you had some questions about the quant section—specifically question 8 of the second Quantitative section of Practice Test 1. Those questions testing our knowledge of Quadrilaterals can be kind of tricky, but never fear, PrepScholar has got your back!

Survey the Question

Let’s search the problem for clues as to what it will be testing, as this will help shift our minds to think about what type of math knowledge we’ll use to solve this question. Pay attention to any words that sound math-specific and anything special about what the numbers look like, and mark them on our paper.

Questions about rectangles and their areas will definitely utilize what we’ve learned about Quadrilaterals. Let’s keep what we’ve learned about this skill at the tip of our minds as we approach this question.

What Do We Know?

Let’s carefully read through the question and make a list of the things that we know.

 

  1. We have a rectangle with a perimeter of $92$ feet
  2. The length is 1 foot greater than twice the width
  3. We want to know the length of the rectangle

 

Develop a Plan

The question tells us that the perimeter of the rectangle is $92$ feet. We know that the perimeter of a polygon is the sum of all of its sides. Since a rectangle has two lengths and two widths, its perimeter is given by the equation:

$$\Perimeter = 2·\Length + 2·\Width$$

The question also gives us an algebraic word sentence describing the relationship between the length and width of the rectangle. It tells us that the length is 1 foot more than twice the width, which we can translate into a math equation as:

$$\Length = 2·\Width+1$$

Let’s solve these two equations simultaenously, and then we’ll be able to compare the length that we calculate to the answer choices.

Solve the Question

Since we already have one equation that is solved for Length, let’s use it to directly substitute into our equation for the perimeter.

$2·\Length+2·\Width$ $=$ $\Perimeter$
$ $ $ $
$2·(2·\Width+1)+2·\Width$ $=$ $92 \feet$
$ $ $ $
$4·\Width+2+2·\Width$ $=$ $92 \feet$
$ $ $ $
$2+6·\Width$ $=$ $92 \feet$

Very nicely done so far. Alright, let’s subtract 2 from both sides of this equation, then we can divide both sides of the equation by $6$ to finish solving for Width.

$2+6·\Width$ $=$ $92 \feet$
$ $ $ $
$6·\Width$ $=$ $90 \feet$
$ $ $ $
$\Width$ $=$ $15 \feet$

Great! Now we can use our equation that’s already solved for Length in terms of Width to calculate Length.

$\Length$ $=$ $2·\Width+1 \feet$
$ $ $ $
$\Length$ $=$ $2·15 +1 \feet$
$ $ $ $
$\Length$ $=$ $30+1 \feet$
$ $ $ $
$\Length$ $=$ $31 \feet$

The correct answer is D, $31$ feet.

What Did We Learn

While it might have been tempting to just guess a couple of values for the length and then check to see if they satisfy the equations described in the question, turns out that actually translating the words into equations, then solving those equations,
was a very efficient and effective solution method.

 

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