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

## Example Questions

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

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

Explanation:

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

Substitute both diagonals in the equation and simplify.

### Example Question #2 : 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.

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

Using the rhombus shown above, find the length of side

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

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

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 #222 : Quadrilaterals

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

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 #1 : 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.

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 #3 : 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.

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 #6 : How To Find The Length Of The Side Of A Rhombus

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

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 #7 : 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.

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 #6 : 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.

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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