Question

jamie is making a pendant out of the rhombus - shaped stone below. she needs to know the perimeter of the stone so she can make the mounting.
if ac is 72 mm and db is 30 mm, what is the perimeter, in millimeters, of the stone?
5 of 10 questions
204
156
39
102

Explanation:

Step1: Find the lengths of the half - diagonals

In a rhombus, the diagonals bisect each other.
If \(AC = 72\) mm, then \(AO=\frac{AC}{2}=\frac{72}{2}=36\) mm.
If \(DB = 30\) mm, then \(BO=\frac{DB}{2}=\frac{30}{2}=15\) mm.

Step2: Use the Pythagorean theorem to find the side length of the rhombus

In right - triangle \(ABO\) (where \(O\) is the intersection point of the diagonals), by the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) (here \(a = AO\), \(b = BO\), and \(c=AB\)).
\(AB=\sqrt{AO^{2}+BO^{2}}=\sqrt{36^{2}+15^{2}}=\sqrt{1296 + 225}=\sqrt{1521}=39\) mm.

Step3: Calculate the perimeter of the rhombus

The perimeter \(P\) of a rhombus is \(P = 4s\) (where \(s\) is the side length of the rhombus).
Since \(s = 39\) mm, \(P=4\times39 = 156\) mm.

Answer:

156