To find the length of the other diagonal of the rhombus, follow these steps:
1. Understand the formula for the area of a rhombus:
The area [tex]\( A \)[/tex] of a rhombus can be calculated using the lengths of its diagonals [tex]\( d_1 \)[/tex] and [tex]\( d_2 \)[/tex]. The formula is:
[tex]\[
A = \frac{1}{2} \times d_1 \times d_2
\][/tex]
2. Given values:
- The area [tex]\( A \)[/tex] of the rhombus is 360 cm².
- The length of one diagonal [tex]\( d_1 \)[/tex] is 24 cm.
3. Rearrange the formula to solve for the other diagonal [tex]\( d_2 \)[/tex]:
Start with the area formula:
[tex]\[
A = \frac{1}{2} \times d_1 \times d_2
\][/tex]
To find [tex]\( d_2 \)[/tex], rearrange the formula to isolate [tex]\( d_2 \)[/tex]:
[tex]\[
d_2 = \frac{2 \times A}{d_1}
\][/tex]
4. Plug in the given values:
- Area [tex]\( A = 360 \)[/tex] cm²
- Diagonal [tex]\( d_1 = 24 \)[/tex] cm
Substitute these values into the rearranged formula:
[tex]\[
d_2 = \frac{2 \times 360}{24}
\][/tex]
5. Calculate the result:
[tex]\[
d_2 = \frac{720}{24} = 30 \, \text{cm}
\][/tex]
So, the length of the other diagonal [tex]\( d_2 \)[/tex] is 30 cm.
