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 area formula

The area formula for a rhombus is $A=\frac{1}{2}d_1d_2$, where $A$ is the area, $d_1$ and $d_2$ are the lengths of the diagonals.

Step2: Substitute known values

We know that $A = 45$ square - kilometers and $d_1=9$ kilometers. Substituting into the formula gives $45=\frac{1}{2}\times9\times d_2$.

Step3: Solve for $d_2$

First, simplify the right - hand side of the equation: $\frac{1}{2}\times9\times d_2=\frac{9d_2}{2}$. Then, solve the equation $45=\frac{9d_2}{2}$ for $d_2$. Multiply both sides of the equation by 2 to get $90 = 9d_2$. Divide both sides by 9, so $d_2 = 10$ kilometers.

Answer:

10