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ISEE Upper Level Math : How to find the length of the side of a rhombus

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Example Questions

Example Question #1 : Rhombuses

A rhombus has a perimeter of $36\ in$ . Give the side length of the rhombus.

Possible Answers:

$10\ in$

$12\ in$

$6\ in$

$8\ in$

$9\ in$

Correct answer:

$9\ in$

Explanation:

Like any polygon, the perimeter of the rhombus is the total distance around the outside, which can be found by adding together the length of each side. In the case of a rhombus, all four sides have the same length, i.e.

Perimeter=4a ,

where is the length of each side.

$Perimeter=4a\Rightarrow 36=4a\Rightarrow a=9\ in$

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Example Question #291 : Plane Geometry

A rhombus has the area of $9\sqrt{2}\ cm^2$ . One of the interior angles is $45^{\circ}$ . Give the length of each side of the rhombus.

Possible Answers:

$2\sqrt{2}\ cm$

$3\ cm$

$2\ cm$

$3\sqrt{2}\ cm$

$3\sqrt{3}\ cm$

Correct answer:

$3\sqrt{2}\ cm$

Explanation:

The area of a rhombus can be determined by the following formula:

$Area=s^2sin\alpha$ ,

where is the length of any side and $\alpha$ is any interior angle.

$Area=s^2sin\alpha\Rightarrow 9\sqrt{2}=s^2\times sin45^{\circ}\Rightarrow 9\sqrt{2}=s^2 \times \frac{\sqrt{2}}{2}$

$\Rightarrow s^2=18\Rightarrow s=\sqrt{18}=\sqrt{9\times 2}=3\sqrt{2}\ cm$

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All ISEE Upper Level Math Resources

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ISEE Upper Level Math : How to find the length of the side of a rhombus

Study concepts, example questions & explanations for ISEE Upper Level Math

All ISEE Upper Level Math Resources

Example Questions

Example Question #1 : Rhombuses

Example Question #291 : Plane Geometry

All ISEE Upper Level Math Resources

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