Question

find the value of $x$ to the nearest tenth.

Explanation:

Step1: Calculate the area of the triangle

The area of a right - triangle is given by \(A=\frac{1}{2}\times base\times height\). Here, the base is \(5\) and the height is \(6\), so \(A = \frac{1}{2}\times5\times6=15\).

Step2: Relate the area of the triangle to the parallelogram

The area of the parallelogram is also \(A = base\times height\). The base of the parallelogram is \(8\) and the height is \(x\). Since the area of the parallelogram is equal to the area of the triangle (they are related in the figure), we have the equation \(8x=15\).

Step3: Solve for \(x\)

From \(8x = 15\), we can solve for \(x\) by dividing both sides of the equation by \(8\). So \(x=\frac{15}{8}=1.875\).

Answer:

\(1.9\)