SAT Math : How to find the perimeter of a rhombus

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #1 : Rhombuses

If the area of a rhombus is 24 and one diagonal length is 6, find the perimeter of the rhombus.

Possible Answers:

16

12

8

24

20

Correct answer:

20

Explanation:

The area of a rhombus is found by

A = 1/2(d1)(d2)

where d1 and d2 are the lengths of the diagonals.  Substituting for the given values yields

24 = 1/2(d1)(6)

24 = 3(d1)

8 = d1

Now, use the facts that diagonals are perpendicular in a rhombus, diagonals bisect each other in a rhombus, and the Pythagorean Theorem to determine that the two diagonals form 4 right triangles with leg lengths of 3 and 4.  Since 32 + 42 = 52, each side length is 5, so the perimeter is 5(4) = 20.

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