Question

the area of this rhombus is 45 square meters. one of its diagonals is 15 meters. what is the length of the missing diagonal, d?

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 $A = 45$ square - meters and $d_1=15$ meters. Substitute into the formula: $45=\frac{1}{2}\times15\times d_2$.

Step3: Solve for $d_2$

First, simplify the right - hand side of the equation: $\frac{1}{2}\times15\times d_2=\frac{15d_2}{2}$. Then we have the equation $45=\frac{15d_2}{2}$. Multiply both sides by 2 to get $90 = 15d_2$. Divide both sides by 15: $d_2=\frac{90}{15}=6$ meters.

Answer:

6