### All SAT Math Resources

## Example Questions

### Example Question #71 : Quadrilaterals

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

**Possible Answers:**

16

8

12

24

20

**Correct answer:**

20

Explanation:

The area of a rhombus is found by

*A* = 1/2(*d*_{1})(*d*_{2})

where *d*_{1} and *d*_{2} are the lengths of the diagonals. Substituting for the given values yields

24 = 1/2(*d*_{1})(6)

24 = 3(*d*_{1})

8 = *d*_{1}

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 3^{2} + 4^{2} = 5^{2}, each side length is 5, so the perimeter is 5(4) = 20.

Nick

Certified Tutor

Certified Tutor

Kalamazoo College, Bachelors, Chemistry. University of Michigan-Ann Arbor, Masters, Inorganic Chemistry.