ACT Math : How to find the length of the side of a rhombus

Study concepts, example questions & explanations for ACT Math

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Example Questions

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Example Question #21 : Rhombuses

If the diagonals of a rhombus were  and , what is the side length of the rhombus?

Possible Answers:

Correct answer:

Explanation:

Write the formula used to find the rhombus side length given 2 diagonals.

Substitute both diagonals in the equation and simplify.

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

A rhombus has a perimeter of . Find the length for one side of the rhombus.

Possible Answers:

Correct answer:

Explanation:

The perimeter formula for a rhombus is the same formula used to find the perimeter of a square. This is because both shapes, by definition, have  equivalent sides. Thus, the total perimeter is the sum of all  sides. 

To solve this problem, apply the perimeter formula for a rhombus: 
By applying the perimeter formula, the solution is:





Example Question #22 : Rhombuses

Rhombus custom vt

Using the rhombus shown above, find the length of side 

Possible Answers:

Correct answer:

Explanation:

The perimeter formula for a rhombus is the same formula used to find the perimeter of a square. This is because both shapes, by definition, have  equivalent sides. Thus, the total perimeter is the sum of all  sides. 

To solve this problem, apply the perimeter formula for a rhombus: 
By applying the perimeter formula, the solution is:





Check: 

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

Rhombus custom vt

A rhombus has two perpendicular interior diagonal lines. The diagonals have lengths of   and . Find the length for side

Possible Answers:

Correct answer:

Explanation:

This problem provides the lengths of the two perpendicular interior diagonal lines in the rhombus. To use this information to find the length of one side of the rhombus, apply the formula:  



where  the length of one side, and both  and  each represent one of the perpendicular diagonal lines. 

The solution is: 

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

The perimeter of a rhombus is equal to . Find the length for one side of the rhombus. 

Possible Answers:

Correct answer:

Explanation:

To solve this problem, apply the perimeter formula for a rhombus: 
Note that the perimeter formula for a rhombus is the same formula used to find the perimeter of a square. This is because both shapes, by definition, have  equivalent sides. The total perimeter is the sum of all  sides. 

The primary differentiation between rhombuses and squares is that latter must have four interior right angles. Although the four interior angles of a rhombus must also equal a sum of 360 degrees, the interior angles inside of a rhombus do not need to be right angles. Instead, the adjacent interior angles of a rhombus must be supplementary angles.

By applying the perimeter formula, the solution is: 







Check:



     

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

A rhombus has two perpendicular interior diagonal lines, each with endpoints that are the vertex of opposite interior angles. The diagonals have lengths of   and . Find the length for one side of the rhombus. 

Possible Answers:

Correct answer:

Explanation:

This problem provides the lengths of the two perpendicular interior diagonal lines in the rhombus. To use this information to find the length of one side of the rhombus, apply the formula:  



where  the length of one side, and both  and  each represent one of the perpendicular diagonal lines. 

The solution is:

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

A rhombus has a perimeter of  inches. Find the length for one side of the rhombus. 

Possible Answers:

 

Correct answer:

Explanation:

To solve this problem, apply the perimeter formula for a rhombus: .

Note that the perimeter formula for a rhombus is the same formula used to find the perimeter of a square. This is because both shapes, by definition, have  equivalent sides. The total perimeter is the sum of all  sides. 

The primary differentiation between rhombuses and squares is that latter must have four interior right angles. Although the four interior angles of a rhombus must also equal a sum of 360 degrees, the interior angles inside of a rhombus do not need to be right angles. Instead, the adjacent interior angles of a rhombus must be supplementary angles.

By applying the perimeter formula, the solution is: 

, where  is equal to one of the four sides. 

 

 is equal to  inches. Since  inch is equal to  foot, the final answer is:


 inches is equal to  foot, which can be reduced to  foot

Example Question #7 : How To Find The Length Of The Side Of A Rhombus

Rhombus custom vt

Using the rhombus shown above, find the length of side .

Possible Answers:

Correct answer:

Explanation:

To solve this problem, apply the perimeter formula for a rhombus: 
Note that the perimeter formula for a rhombus is the same formula used to find the perimeter of a square. This is because both shapes, by definition, have  equivalent sides. The total perimeter is the sum of all  sides. 

The primary differentiation between rhombuses and squares is that latter must have four interior right angles. Although the four interior angles of a rhombus must also equal a sum of 360 degrees, the interior angles inside of a rhombus do not need to be right angles. Instead, the adjacent interior angles of a rhombus must be supplementary angles.
By applying the perimeter formula, the solution is:





Check:

Example Question #8 : How To Find The Length Of The Side Of A Rhombus

A rhombus has two perpendicular interior diagonal lines, each with endpoints that are the vertex of opposite interior angles. The diagonals have lengths of   and . Find the length for one side of the rhombus. 

Possible Answers:

Correct answer:

Explanation:

This problem provides the lengths of the two perpendicular interior diagonal lines in the rhombus. To use this information to find the length of one side of the rhombus, apply the formula:  



where  the length of one side, and both  and  each represent one of the perpendicular diagonal lines. 

The solution is: 

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

A rhombus has two perpendicular interior diagonal lines, each with endpoints that are the vertex of opposite interior angles. The diagonals have lengths of   and . Find the length for one side of the rhombus. 

Possible Answers:

Correct answer:

Explanation:

This problem provides the lengths of the two perpendicular interior diagonal lines in the rhombus. To use this information to find the length of one side of the rhombus, apply the formula:  



where  the length of one side, and both  and  each represent one of the perpendicular diagonal lines. 

The solution is: 

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