Basic Geometry : How to find the length of the side of a rectangle

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #11 : How To Find The Length Of The Side Of A Rectangle

If the perimeter of a rectangle is \(\displaystyle 20\), and the length of the rectangle is \(\displaystyle 9\), what is the width of the rectangle?

Possible Answers:

\(\displaystyle 2\)

\(\displaystyle 1\)

\(\displaystyle 11\)

\(\displaystyle 5\)

Correct answer:

\(\displaystyle 1\)

Explanation:

Recall how to find the perimeter of a rectangle.

\(\displaystyle \text{Perimeter}=2(\text{length}+\text{width})\)

We can then manipulate this equation to find the width.

\(\displaystyle \text{length}+\text{width}=\frac{\text{Perimeter}}{2}\)

\(\displaystyle \text{width}=\frac{\text{Perimeter}}{2}-\text{length}\)

Now, plug in the information given by the question to find the width.

\(\displaystyle \text{width}=\frac{20}{2}-9=10-9=1\)

Example Question #71 : Quadrilaterals

If the perimeter of the rectangle is \(\displaystyle 54\), and the length of the rectangle is \(\displaystyle 12\), what is the width of the rectangle?

Possible Answers:

\(\displaystyle 15\)

\(\displaystyle 14\)

\(\displaystyle 13\)

\(\displaystyle 17\)

Correct answer:

\(\displaystyle 15\)

Explanation:

Recall how to find the perimeter of a rectangle.

\(\displaystyle \text{Perimeter}=2(\text{length}+\text{width})\)

We can then manipulate this equation to find the width.

\(\displaystyle \text{length}+\text{width}=\frac{\text{Perimeter}}{2}\)

\(\displaystyle \text{width}=\frac{\text{Perimeter}}{2}-\text{length}\)

Now, plug in the information given by the question to find the width.

\(\displaystyle \text{width}=\frac{54}{2}-12=27-12=15\)

Example Question #13 : How To Find The Length Of The Side Of A Rectangle

If the perimeter of a rectangle is \(\displaystyle 22\), and the length of the rectangle is \(\displaystyle 5\), what is the width of the rectangle?

Possible Answers:

\(\displaystyle 7\)

\(\displaystyle 5\)

\(\displaystyle 4\)

\(\displaystyle 6\)

Correct answer:

\(\displaystyle 6\)

Explanation:

Recall how to find the perimeter of a rectangle.

\(\displaystyle \text{Perimeter}=2(\text{length}+\text{width})\)

We can then manipulate this equation to find the width.

\(\displaystyle \text{length}+\text{width}=\frac{\text{Perimeter}}{2}\)

\(\displaystyle \text{width}=\frac{\text{Perimeter}}{2}-\text{length}\)

Now, plug in the information given by the question to find the width.

\(\displaystyle \text{width}=\frac{22}{2}-5=11-5=6\)

Example Question #11 : How To Find The Length Of The Side Of A Rectangle

If the perimeter of the rectangle is \(\displaystyle 24\), and the width of the rectangle is \(\displaystyle 10\), what is the length of the rectangle?

Possible Answers:

\(\displaystyle 8\)

\(\displaystyle 2\)

\(\displaystyle 14\)

\(\displaystyle 3\)

Correct answer:

\(\displaystyle 2\)

Explanation:

Recall how to find the perimeter of a rectangle.

\(\displaystyle \text{Perimeter}=2(\text{length}+\text{width})\)

We can then manipulate this equation to find the length.

\(\displaystyle \text{length}+\text{width}=\frac{\text{Perimeter}}{2}\)

\(\displaystyle \text{length}=\frac{\text{Perimeter}}{2}-\text{width}\)

Now, plug in the information given by the question to find the length.

\(\displaystyle \text{length}=\frac{24}{2}-10=12-10=2\)

Example Question #15 : How To Find The Length Of The Side Of A Rectangle

If the perimeter of a rectangle is \(\displaystyle 200\), and the width of the rectangle is \(\displaystyle 54\), what is the length of the rectangle?

Possible Answers:

\(\displaystyle 58\)

\(\displaystyle 46\)

\(\displaystyle 61\)

\(\displaystyle 45\)

Correct answer:

\(\displaystyle 46\)

Explanation:

Recall how to find the perimeter of a rectangle.

\(\displaystyle \text{Perimeter}=2(\text{length}+\text{width})\)

We can then manipulate this equation to find the length.

\(\displaystyle \text{length}+\text{width}=\frac{\text{Perimeter}}{2}\)

\(\displaystyle \text{length}=\frac{\text{Perimeter}}{2}-\text{width}\)

Now, plug in the information given by the question to find the length.

\(\displaystyle \text{length}=\frac{200}{2}-54=100-54=46\)

Example Question #16 : How To Find The Length Of The Side Of A Rectangle

If the perimeter of the rectangle is \(\displaystyle 56\), and the width of the rectangle is \(\displaystyle 12\), what is the length of the rectangle?

Possible Answers:

\(\displaystyle 18\)

\(\displaystyle 15\)

\(\displaystyle 16\)

\(\displaystyle 12\)

Correct answer:

\(\displaystyle 16\)

Explanation:

Recall how to find the perimeter of a rectangle.

\(\displaystyle \text{Perimeter}=2(\text{length}+\text{width})\)

We can then manipulate this equation to find the length.

\(\displaystyle \text{length}+\text{width}=\frac{\text{Perimeter}}{2}\)

\(\displaystyle \text{length}=\frac{\text{Perimeter}}{2}-\text{width}\)

Now, plug in the information given by the question to find the length.

\(\displaystyle \text{length}=\frac{56}{2}-12=28-12=16\)

Example Question #17 : How To Find The Length Of The Side Of A Rectangle

If the perimeter of a rectangle is \(\displaystyle 64\), and the width of the rectangle is \(\displaystyle 17\), what is the length of the rectangle?

Possible Answers:

\(\displaystyle 17\)

\(\displaystyle 13\)

\(\displaystyle 15\)

\(\displaystyle 14\)

Correct answer:

\(\displaystyle 15\)

Explanation:

Recall how to find the perimeter of a rectangle.

\(\displaystyle \text{Perimeter}=2(\text{length}+\text{width})\)

We can then manipulate this equation to find the length.

\(\displaystyle \text{length}+\text{width}=\frac{\text{Perimeter}}{2}\)

\(\displaystyle \text{length}=\frac{\text{Perimeter}}{2}-\text{width}\)

Now, plug in the information given by the question to find the length.

\(\displaystyle \text{length}=\frac{64}{2}-17=32-17=15\)

Example Question #18 : How To Find The Length Of The Side Of A Rectangle

If the perimeter of a rectangle is \(\displaystyle 66\), and the width of the perimeter is \(\displaystyle 15\), what is the length of the rectangle?

Possible Answers:

\(\displaystyle 16\)

\(\displaystyle 51\)

\(\displaystyle 18\)

\(\displaystyle 14\)

Correct answer:

\(\displaystyle 18\)

Explanation:

Recall how to find the perimeter of a rectangle.

\(\displaystyle \text{Perimeter}=2(\text{length}+\text{width})\)

We can then manipulate this equation to find the length.

\(\displaystyle \text{length}+\text{width}=\frac{\text{Perimeter}}{2}\)

\(\displaystyle \text{length}=\frac{\text{Perimeter}}{2}-\text{width}\)

Now, plug in the information given by the question to find the length.

\(\displaystyle \text{length}=\frac{66}{2}-15=33-15=18\)

Example Question #19 : How To Find The Length Of The Side Of A Rectangle

If the perimeter of a rectangle is \(\displaystyle 96\), and the width of the rectangle is \(\displaystyle 46\), what is the length of the rectangle?

Possible Answers:

\(\displaystyle 2\)

\(\displaystyle 50\)

\(\displaystyle 8\)

\(\displaystyle 36\)

Correct answer:

\(\displaystyle 2\)

Explanation:

Recall how to find the perimeter of a rectangle.

\(\displaystyle \text{Perimeter}=2(\text{length}+\text{width})\)

We can then manipulate this equation to find the length.

\(\displaystyle \text{length}+\text{width}=\frac{\text{Perimeter}}{2}\)

\(\displaystyle \text{length}=\frac{\text{Perimeter}}{2}-\text{width}\)

Now, plug in the information given by the question to find the length.

\(\displaystyle \text{length}=\frac{96}{2}-46=48-46=2\)

Example Question #20 : How To Find The Length Of The Side Of A Rectangle

If the area of a rectangle is \(\displaystyle 45\), and the length of the rectangle is \(\displaystyle 9\), what is the width of the rectangle?

Possible Answers:

\(\displaystyle 6\)

\(\displaystyle 7\)

\(\displaystyle 4\)

\(\displaystyle 5\)

Correct answer:

\(\displaystyle 5\)

Explanation:

Recall how to find the area of a rectangle.

\(\displaystyle \text{Area}=\text{length}\times\text{width}\)

We can divide both sides by the length to find the width.

\(\displaystyle \text{Width}=\frac{\text{Area}}{\text{length}}\)

Now, plug in the information from the question.

\(\displaystyle \text{Width}=\frac{45}{9}=5\)

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