52.8k views
0 votes
The diagonals of rhombus WXYZ intersect at point P. If WP = 12 and XP = 5, find the perimeter of the rhombus.

User Joeln
by
8.2k points

2 Answers

5 votes

Final answer:

The perimeter of the rhombus is found by first determining the length of one of its sides using the given halves of the diagonals, WP = 12 and XP = 5, and the Pythagorean theorem. The length of one side is found to be 13, and since there are four sides, the perimeter is 52 units.

Step-by-step explanation:

To find the perimeter of the rhombus, we start by recognizing that all sides of a rhombus are of equal length. The diagonals intersect at point P and bisect each other at right angles. Given that WP = 12 and XP = 5, we can say that the entire length of one diagonal WZ (2 * WP) is 24 and the entire length of the other diagonal XY (2 * XP) is 10. Since the diagonals bisect each other at a right angle, they form four right triangles within the rhombus.

In one of these right triangles, the sides WP and XP are the legs, and the hypotenuse would be a side of the rhombus, which we can call 's'. Using the Pythagorean theorem:

s² = WP² + XP²

s² = 12² + 5²

s² = 144 + 25

s² = 169

s = √169

s = 13

Since a rhombus has four sides of equal length, the perimeter (P) is four times the length of one side (s).

P = 4s = 4(13) = 52

Therefore, the perimeter of the rhombus is 52 units.

User Marc Wittke
by
8.2k points
4 votes
A rhombus is a geometrical figure wherein the diagonals intersect making a right angle. Given that the sides of the formed triangles from the intersection are 12 and 5, calculate the hypotenuse using the Pythagorean Theorem.

c^2 = 12^2 + 5^2

where c is the length of hypotenuse. c then is 13. The hypotenuse is also the measure of four equal sides of the rhombus. Multiply this value by 4 to obtain the perimeter. Thus, the perimeter of the rhombus is 52 units.
User Bhavik
by
8.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.