To find the length of the other diagonal of the rhombus, we can use the formula that relates the area of a rhombus to its diagonals. For a rhombus, the area (A) can be calculated using the lengths of its diagonals (d1 and d2):
\[ A = \frac{1}{2} \times d1 \times d2 \]
Given:
- One diagonal (d1) = 10 cm
- The area (A) = 230 cm²
We need to find the length of the other diagonal (d2).
Using the formula for the area, we can plug in the given values and solve for d2:
\[ 230 = \frac{1}{2} \times 10 \times d2 \]
To solve for d2, first multiply both sides of the equation by 2 to get rid of the fraction:
\[ 460 = 10 \times d2 \]
Now, divide both sides by 10 to isolate d2:
\[ d2 = \frac{460}{10} \]
\[ d2 = 46 \text{ cm} \]
So, the length of the other diagonal of the rhombus is 46 cm.
