the lenghts of the diagonals of a rhombus are 16cm and 12cm respectively.find the lenght of each of the sides
the diagonals of a rhombus are of length 16cm and 12cm. find the lenght of its sides
To find the length of each side of a rhombus given the lengths of the diagonals, you can use the following formula:
\[ \text{Side length} = \frac{\sqrt{\text{Diagonal 1}^2 + \text{Diagonal 2}^2}}{2} \]
In this case, the diagonals are given as 16 cm and 12 cm. Let's substitute these values into the formula and calculate the side length:
\[ \text{Side length} = \frac{\sqrt{16^2 + 12^2}}{2} \]
\[ \text{Side length} = \frac{\sqrt{256 + 144}}{2} \]
\[ \text{Side length} = \frac{\sqrt{400}}{2} \]
\[ \text{Side length} = \frac{20}{2} \]
\[ \text{Side length} = 10 \]
Therefore, each side of the rhombus has a length of 10 cm.
Hint: The diagonals of a rhombus right-bisect each other.
Another hint: Make a sketch. What type of triangles do you see?
Do you know the legs of those triangles?