Question

the figure shown has a total area of 53 square units. which equation can be used to find the value of x? 53 = 3·4x + 5·8 53 = 5·x + 8·4 53 = 3·x + 5·4 53 = 3·x + 8·4

Explanation:

Step1: Analyze the figure's area

The figure can be divided into two rectangles. One rectangle has dimensions \(3\) and \(x\), and the other has dimensions \(8\) and \(4\). The area of a rectangle is length times width. So the total area is the sum of the areas of these two rectangles.

Step2: Formulate the area equation

The area of the first rectangle (with sides \(3\) and \(x\)) is \(3\times x = 3\cdot x\). The area of the second rectangle (with sides \(8\) and \(4\)) is \(8\times 4 = 8\cdot 4\). The total area is \(53\), so the equation is \(53 = 3\cdot x + 8\cdot 4\).

Answer:

\(53 = 3\cdot x + 8\cdot 4\) (the fourth option: \(53 = 3\cdot x + 8\cdot 4\))