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 the area formula for the shaded region

The area of the shaded rhombus is half of the area of the rectangle. Let the area of the rectangle be \(A = 15\times x\). Then the area of the rhombus \(A_{rhombus}=\frac{1}{2}\times(15\times x)\)

Step2: Set up the equation

Since \(A_{rhombus} = 60\), we have the equation \(\frac{1}{2}\times(15\times x)=60\)

Step3: Solve the equation for \(x\)

Multiply both sides of the equation by \(2\): \(15\times x=120\)
Then divide both sides by \(15\): \(x=\frac{120}{15}=8\)

Answer:

8 units