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 )?

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 the diagonals.

Step2: Substitute known values

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

Step3: Solve for $d$

First, multiply both sides by 2:
$45 \times 2 = 9 \times d$
$90 = 9d$
Then divide both sides by 9:
$d = \frac{90}{9}$

Answer:

10 kilometers