Okay so let's take this all apart into smaller pieces and work this out together. Let's call the length y and the width x. So we know that 2y + 2x = 38 since the perimeter is 38. We also know that the length is six inches less than four times the width. In an equation using x's and y's, this can be expressed as y = 4x - 6. Now we have two unknown variables, x and y or the length and the width, and we have two equations thus we can solve for each variable.
First, we can replace y in the 2y + 2x = 38 equation with 4x - 6. We already showed that that is what y is equivalent to so it's perfectly logical and mathematically legal to substitute any y we see with 4x - 6. This makes the first equation to be: 2 (4x - 6) + 2x = 28. Now we can simply solve for x as shown in the following:
2 (4x - 6) + 2x = 38
8x - 12 + 2x = 38
10x - 12 = 38
10x = 50
x = 5
So now that we know that x = 5, we can plug it back in to one of our two initial equations to solve for x. It doesn't matter which one, they both should result in the same y-value. I will show you how to do it using both equations.
First one: 2y + 2x = 38
2y + 2(5) = 38
2y + 10 = 38
2y = 28
y = 14
Second equation: Y = 4x - 6
y = 4(5) - 6
y = 20 - 6
y = 14
As you can see, in both cases, y = 14 meaning that y truly does equal 14.
So what we are trying to look for is the area of this rectangle. Area of a rectangle is found by multiplying the length by the width or, in our case, x * y. Therefore we simply multiply 5 and 14 together or 5 * 14 = 70. And since the units are in inches, the area is 70 squared inches.