if the diagonals of a rhombus is 12 and 16 what is the measure of a side of the rhombus 5,,20,10 square root 3
The diagonals of a rhombus intersect at right angles. So the two half diagonals and one side form a right triangle, with lengths: (12/2)=6, (16/2)=8,
What is the length of a side (hypotenuse).
Hint: use Pythagoras theorem.
To find the measure of a side of the rhombus, we can use the Pythagorean theorem.
In a rhombus, the diagonals are perpendicular bisectors of each other, and they divide the rhombus into four congruent right-angled triangles.
Let's assume that the side of the rhombus is "x". The diagonals of the rhombus create four congruent right-angled triangles.
Using the Pythagorean theorem, we have:
(1st triangle)
Side 1: x
Side 2: x/2 (half of one diagonal)
Hypotenuse: 12
(x²) + (x/2)² = 12²
Simplifying:
x² + (x/2)² = 144
x² + x²/4 = 144
4x² + x² = 4 * 144
5x² = 576
x² = 576/5
x² = 115.2
Taking the square root of both sides:
x = √115.2
x ≈ 10.74
Therefore, the measure of one side of the rhombus is approximately 10.74 units.