If the lengths of the diagonals of a rhombus are 6 and 8, the perimeter of the rhombus is..?and how do you?

Question

solve

Answer 1

20

Proof:

Since a rhombus is also a parallelogram, you know that the opposite angles are congruent. You also know that the diagonals bisect each other.

Since the sides are all equal in length, you know that the bisectors intersect at right angles.

You can use the Pythagorus Theorem at this point. The diagonals are divided so that they form the legs of a right triangle with legs 3 and 4 long. The hypotenuse is 5 long.

Since a rhombus has all four sides the same length, the perimeter is 20.

Answer 2

The perimeter of the rhombus is 20.

The way you get at this is by knowing the diagonals will be perpendicular bisectors of each other. By knowing this, you now have four right triangles with sides of 3, 4, and x. This is a commonly known right triangle (3, 4, 5). Therefore, the four sides (of equal length) are each 5. The perimeter is 5 * 4 = 20.

Answer 3

perimeter = 4x5 = 20

Reason: The diagonals of a rhombus are the perpendicular bisectors for each other. Therefore, you can dissect the rhombus into 4 congruent right triangles with legs 3 and 4. By Pythagorean theorem, the hypotenuse, which is one of the four congruent sides of the rhombus, is 5.