Question

the shaded figure is a rhombus. the area of the shaded section is 60 square units. what is the value of x?
○ 4 units
○ 6 units
○ 8 units
○ 9 units

Explanation:

Step1: Recall rhombus area formula

The area of a rhombus is given by \( A=\frac{d_1\times d_2}{2} \), where \( d_1 \) and \( d_2 \) are the lengths of the diagonals. From the diagram, the diagonals of the rhombus are equal to the length and width of the rectangle, so \( d_1 = 15 \) and \( d_2=x \), and the area \( A = 60 \).

Step2: Substitute into the formula

Substitute \( A = 60 \) and \( d_1=15 \) into the formula \( A=\frac{d_1\times d_2}{2} \):
\[
60=\frac{15\times x}{2}
\]

Step3: Solve for x

Multiply both sides by 2:
\[
120 = 15x
\]
Divide both sides by 15:
\[
x=\frac{120}{15}=8
\]

Answer:

8 units (corresponding to the option "8 units")