We want to find the width of a rectangle. We can write a system of linear equations and solve it for the width of the rectangle. First, let's recall the formula for the perimeter of a rectangle.
P=2l+2w
In this formula, P is the perimeter of the rectangle, l is the length, and w is the width. We know from the exercise that the perimeter of the rectangle is 72 feet. We also know that the length of our rectangle is 8 feet more that its width.
l=w+ 8
Now let's create a system of linear equations. We will rewrite the formula for the perimeter of the rectangle to isolate l on one side of the equation. Let's do it!
Now we are ready to write the system of equations.
l=36-w & (I) l=w+8 & (II)
Next, we will graph each equation and look for a point of intersection, which will be the solution to the system of equations.
The graphs seem to intersect at the point (14,22). Finally, let's check if this point is a solution to the system of equations we createdby substituting 14 for w and 22 for l in each equation and checking to see if they produce true statements.
