Question

the area of this rhombus is 20 square miles. one of its diagonals is 10 miles. what is the length of the missing diagonal, d? miles

Explanation:

Step1: Recall area formula

The area formula of 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 $A = 20$ square - miles and $d_1=10$ miles. Substituting into the formula gives $20=\frac{1}{2}\times10\times d_2$.

Step3: Solve for $d_2$

First, simplify the right - hand side of the equation: $\frac{1}{2}\times10\times d_2 = 5d_2$. So, $20 = 5d_2$. Then divide both sides by 5: $d_2=\frac{20}{5}=4$ miles.

Answer:

4