the diagonals of a rhombus have the lengths 6 and 8 centimeters. whats the number of centimeters of the perimeter of the rhombus?
in a rhombus, the diagonals are perpendicular , so if you divide each diagonal in half (where they intersect) than you get a right triangle with sides 3 4 and x. Use pythagorean theorum and that side is 5. Because all sides of a rhombus are congruent, each side is 5, so the perimeter is 20. Hope i helped!:)
To find the perimeter of a rhombus, we need to know the length of one side. However, we can find the length of the side using the given information about the diagonals.
In a rhombus, the diagonals are perpendicular bisectors of each other. This means they divide the rhombus into four congruent right-angled triangles.
Let's consider one of these triangles. The hypotenuse of the triangle is one of the diagonals, which has a length of 8 centimeters. The legs of the right-angled triangle represent half the lengths of the sides of the rhombus.
Using the Pythagorean theorem, we can find the length of each leg. The theorem states that, in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. So, we have:
(leg)^2 + (leg)^2 = (hypotenuse)^2
2(leg)^2 = 8^2
2(leg)^2 = 64
(leg)^2 = 64/2
(leg)^2 = 32
leg = √32
leg ≈ 5.66
Therefore, each leg of the triangle, and consequently each side of the rhombus, has a length of approximately 5.66 centimeters.
Since a rhombus has four congruent sides, the perimeter of the rhombus is equal to 4 times the length of one side:
Perimeter = 4 * side length
Perimeter = 4 * 5.66 centimeters
Perimeter ≈ 22.64 centimeters
Hence, the number of centimeters in the perimeter of the rhombus is approximately 22.64 centimeters.