Question

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: Find length of diagonal AC

Since $EC = 8$, and diagonals of a rhombus bisect each other, $AC = 2 \times EC = 2 \times 8 = 16$ units.

Step2: Use rhombus area formula

Area of rhombus = $\frac{1}{2} \times d_1 \times d_2$, where $d_1=AC$, $d_2=DB$. Substitute known values:
$72 = \frac{1}{2} \times 16 \times (x-1)$

Step3: Simplify and solve for x

First calculate $\frac{1}{2} \times 16 = 8$, so:
$72 = 8(x-1)$
Divide both sides by 8: $9 = x - 1$
Add 1 to both sides: $x = 9 + 1 = 10$

Answer:

B. 10