The diagonals of a rhombus are 16 and 30. What is the perimeter
2 answers:
Answer: 68
Step-by-step explanation: Let's start this problem by drawing the picture of the rhombus which I have attached for you in the image provided.
A rhombus is a quadrilateral that has 4 congruent sides and the diagonals of a rhombus are perpendicular to each other. The diagonals of a rhombus bisect each other so the diagonal that has a length of 16 is split into two segments that each have a length of 8. The diagonal that has a length of 30 is split into two segments that each have a length of 15.
Now, remember that we're asked to find the perimeter of the rhombus which is the sum of the lengths of all the sides. Since the four sides of the rhombus are equal in length, we can give all four sides of the rhombus a length of <em>X.</em>
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To find the value of <em>X</em>, notice that we have a right triangle in the upper right of the figure so the pythagorean theorem tells us that (15)² + (8)² = (x)² which simplifies to 225 + 64 = x² or 289 = x².
Now we can square root both sides to get 17 = x.
This means that the length of each side of our rhombus is 17. Remember that we are asked to find the perimeter of the rhombus which is the sum of the lengths of all the sides so the perimeter is 17 + 17 + 17 + 17 or 68.
Therefore, the perimeter of the rhombus is 68.
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