Intermediate Geometry : Rhombuses

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #51 : Rhombuses

If a rhombus has a base that is \displaystyle \frac{4}{3} times greater than the height and the height of the rhombus is equal to \displaystyle 9, find the length of one side of the rhombus.  

Possible Answers:

\displaystyle 14

\displaystyle \frac{9}{4}

\displaystyle 12

\displaystyle 9

Correct answer:

\displaystyle 12

Explanation:

To find the length of a side of the rhombus, multiply \displaystyle 9 times \displaystyle \frac{4}{3}

Thus, the solution is:

\displaystyle \frac{9}{1}\times\frac{4}{3}=\frac{36}{3}=12

Example Question #52 : Rhombuses

Given that a rhombus has a perimeter of \displaystyle 124, find the length of one side of the rhombus. 

Possible Answers:

\displaystyle 36

\displaystyle 31

\displaystyle 24

\displaystyle 34

Correct answer:

\displaystyle 31

Explanation:

The perimeter of a rhombus is equal to \displaystyle p=4S, where \displaystyle S= the length of one side of the rhombus. 

Since \displaystyle P=124, we can set up the following equation and solve for \displaystyle S.

\displaystyle 124=4\times (S)

\displaystyle S=\frac{124}{4}=31

Example Question #2 : How To Find The Length Of The Side Of A Rhombus

A rhombus has an area of \displaystyle 360 square units and a height of \displaystyle 8. Find the length of one side of the rhombus. 

Possible Answers:

\displaystyle 40

\displaystyle 60

\displaystyle 90

\displaystyle 45

Correct answer:

\displaystyle 45

Explanation:

To find the length of a side of the rhombus, work backwards using the formula: 

\displaystyle A=(base\times height)

Since we are given the area and the height we plug these values in and solve for the base.

\displaystyle 360=(base\times 8)

\displaystyle base=\frac{360}{8}=45

Example Question #1 : How To Find The Length Of The Side Of A Rhombus

A rhombus has an area of \displaystyle 69 square units, and a height of \displaystyle 6. Find the length of one side of the rhombus. 

Possible Answers:

\displaystyle 12

\displaystyle 9.5

\displaystyle 11.5

\displaystyle 6.5

Correct answer:

\displaystyle 11.5

Explanation:

To find the length of a side of the rhombus, work backwards using the area formula: 

\displaystyle Area=(base\times height)

Since we are given the area and the height we plug these values in and solve for the base.

\displaystyle 69=(base\times 6)

\displaystyle base=\frac{69}{6}=11.5

Example Question #3 : How To Find The Length Of The Side Of A Rhombus

A rhombus has a perimeter of \displaystyle 720. Find the length of one side of the rhombus. 

Possible Answers:

\displaystyle 95

\displaystyle 360

\displaystyle 90

\displaystyle 180

Correct answer:

\displaystyle 180

Explanation:

To solve for the length of one side of the rhombus, apply the perimeter formula:

\displaystyle P=4(S)

\displaystyle S= the length of one side of the rhombus. 

Since we are given the area we plug this value in and solve for \displaystyle S.

\displaystyle 720=4(S)

\displaystyle S=\frac{720}{4}=180

Example Question #3 : How To Find The Length Of The Side Of A Rhombus

A rhombus has an area of \displaystyle 39 square units, and an altitude of \displaystyle 3. Find the length of one side of the rhombus. 

Possible Answers:

\displaystyle 1.3

\displaystyle 12

\displaystyle 13

\displaystyle 26

Correct answer:

\displaystyle 13

Explanation:

Since the area is equal to \displaystyle 39 square units, use the formula: 

\displaystyle A=(base\times altitude)


Since we are given the area and the height, we plug these values in and solve for the base.

\displaystyle 39=(base\times 3)

\displaystyle base=\frac{39}{3}=13

Example Question #4 : How To Find The Length Of The Side Of A Rhombus

The perimeter of a rhombus is equal to \displaystyle 520. Find the length of one side of the rhombus. 

Possible Answers:

\displaystyle 222

\displaystyle 113

\displaystyle 260

\displaystyle 130

Correct answer:

\displaystyle 130

Explanation:

Since \displaystyle P=520

The solution is:

\displaystyle P=4(S), where \displaystyle S= the length of one side of the rhombus. 

Thus, 

\displaystyle 520=4(S)

\displaystyle S=\frac{520}{4}=130

Example Question #4 : How To Find The Length Of The Side Of A Rhombus

A rhombus has an area of \displaystyle 645 square units, and an altitude of \displaystyle 15. What is the length of one side of the rhombus?

Possible Answers:

\displaystyle 43

\displaystyle 7.5

\displaystyle 12

\displaystyle 45

Correct answer:

\displaystyle 43

Explanation:

To find the length of a side of the rhombus, work backwards using the area formula: 

\displaystyle Area=(base\times height)

Since we are given the area and the height, we plug these values into the equation and solve for the base.

\displaystyle 645=(base\times 15)

\displaystyle base=\frac{645}{15}=43

Example Question #1 : How To Find The Length Of The Side Of A Rhombus

Given that a rhombus has an area of \displaystyle 85 square units and a height of \displaystyle 5, find the length of one side of the rhombus. 

Possible Answers:

\displaystyle 17

\displaystyle 20

\displaystyle 18

\displaystyle 15

Correct answer:

\displaystyle 17

Explanation:

To find the length of a side of the rhombus, work backwards using the area formula: 

\displaystyle Area=(base\times height)

Since we are given the area and the height, we plug these values into the equation and solve for the base.

\displaystyle 85=(base\times height)

\displaystyle 85=(base\times 5)

\displaystyle base=\frac{85}{5}=17

Example Question #5 : How To Find The Length Of The Side Of A Rhombus

If a rhombus has a perimeter of \displaystyle 14, what is the length of one side of the rhombus? 

Possible Answers:

\displaystyle 3

\displaystyle 3.5

\displaystyle 5

\displaystyle 4.5

Correct answer:

\displaystyle 3.5

Explanation:

To find the length of a side of the rhombus, apply the formula: \displaystyle p=4(S), where \displaystyle S is equal to the length of a side of the rhombus. 

Since we are given the perimeter we plug that value into the equation and solve for \displaystyle S

Therefore the solution is:

\displaystyle 14=4(S)

\displaystyle S=\frac{14}{4}=3.5

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