Question

solve the following by setting up the proper equations to describe the facts given and then carrying out the mathematical calculations to solve for the unknown variable(s). let x represent length and y represent width. enter your answer in (x, y) format.

the length of a rectangle is 3 times the width. the difference between the length and width is 8 feet. determine the rectangles length and width.

Explanation:

Translate the problem statements into equations

Using the Translating Word Problems and Algebraic Modeling knowledge points
Let \(x\) represent the length and \(y\) represent the width of the rectangle.

• "The length of a rectangle is 3 times the width" translates to:

$$x = 3y$$

• "The difference between the length and width is 8 feet" translates to:

$$x - y = 8$$

Solve the system of equations

Using the Systems of Linear Equations knowledge point
Substitute the first equation \(x = 3y\) into the second equation:

$$3y - y = 8$$

$$2y = 8$$

$$y = 4$$

Substitute \(y = 4\) back into the first equation to find \(x\):

$$x = 3(4) = 12$$

The length is \(12\) feet and the width is \(4\) feet.

Answer:

\((12, 4)\)