the area of rhombus abcd is 72 square units. ec = 8 units and db = x - 1. what is the value of x? 9 10 14 16

Explanation:

Step1: Recall area formula of rhombus

The area formula of a rhombus is $A=\frac{1}{2}d_1d_2$, where $d_1$ and $d_2$ are the lengths of the diagonals. In rhombus $ABCD$, the diagonals are $AC$ and $DB$. Given $EC = 8$ units, then $AC=2EC = 16$ units (diagonals of a rhombus bisect each other), and $DB=x - 1$, and $A = 72$ square - units.

Step2: Substitute values into formula

Substitute into $A=\frac{1}{2}d_1d_2$: $72=\frac{1}{2}\times16\times(x - 1)$.

Step3: Solve the equation

First, simplify the right - hand side of the equation: $\frac{1}{2}\times16\times(x - 1)=8(x - 1)$. So the equation becomes $72 = 8(x - 1)$. Then divide both sides by 8: $\frac{72}{8}=x - 1$, which gives $9=x - 1$. Finally, add 1 to both sides: $x=9 + 1=10$.

Answer:

10