lengths of diagonals of a rhombus are 12 cm and 16 cm respectively. Find the length of the side of rhombus.
DIAGONALS: 12 and 16 cm.
The diagonals of a rhombus are perpendicular bisectors of each other
and form 4 congruent right triangles.
The legs of a triangle are: X=12cm/2=6cm, and Y=16cm/2=8 cm.
The length of each side is:S^2=X^2+Y^2=
6^2+8^2=100sq.cm, S=10cm. NOTE:All sides of the rhombus are equal.
To find the length of the side of a rhombus, you can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In a rhombus, the diagonals bisect each other at right angles, forming four right triangles. Let's label the length of one diagonal as "d1" and the length of the other diagonal as "d2".
In this case, d1 = 12 cm and d2 = 16 cm.
To find the length of the side of the rhombus, we need to find the length of the hypotenuse of one of the right triangles formed by the diagonals. Let's call it "s" (for side length).
Using the Pythagorean theorem, we can set up the following equation:
s² = (d1/2)² + (d2/2)²
Substituting the given values:
s² = (12/2)² + (16/2)²
s² = 6² + 8²
s² = 36 + 64
s² = 100
s = √100
s = 10 cm
Therefore, the length of each side of the rhombus is 10 cm.