perimeter of 212 inches and the length is 82 more then the width. What are the dimensions?
P=2L+2W
= 2(W+82)+2w=4W+164
212-164=4W
W=48/4=12
L=82+12
To find the dimensions, we need to set up two equations based on the given information.
Let's consider the length as L and the width as W.
From the given information, we know that the perimeter is 212 inches. The formula for the perimeter of a rectangle is P = 2L + 2W.
So, we have the equation: 2L + 2W = 212.
We also know that the length is 82 more than the width. This can be written as: L = W + 82.
Now we can substitute the value of L into the perimeter equation.
Replacing L with W + 82, we get: 2(W + 82) + 2W = 212.
Expanding and simplifying, we have: 2W + 164 + 2W = 212.
Combining like terms, we get: 4W + 164 = 212.
Subtracting 164 from both sides, we have: 4W = 48.
Dividing both sides by 4, we get: W = 12.
Now, we can substitute the value of W back into the equation for L.
Using L = W + 82, we have: L = 12 + 82.
Simplifying, we get: L = 94.
Therefore, the dimensions of the rectangle are 94 inches for the length and 12 inches for the width.