Question

the area of this rhombus is 45 square kilometers. one of its diagonals is 9 kilometers. what is the length of the missing diagonal, d?
kilometers

Explanation:

Step1: Recall rhombus area formula

The area of a rhombus is given by $A = \frac{1}{2} \times d_1 \times d_2$, where $d_1$ and $d_2$ are the lengths of its diagonals.

Step2: Substitute known values

We know $A=45$ km², $d_1=9$ km. Plug into the formula:
$45 = \frac{1}{2} \times 9 \times d$

Step3: Solve for $d$

First multiply both sides by 2:
$90 = 9 \times d$
Then divide by 9:
$d = \frac{90}{9} = 10$

Answer:

10 kilometers