Question

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

Answer 1

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.

Answer 2

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.