The perimeter of a rectangle is given as

Perimeter = 2(length + width).

Here perimeter is given as 36 inches.

Only option 1 ( l= 9, w= 9) satisfies this perimeter.

Check: perimeter = 2(9+9) = 2*18= 36. Inches.

All other options would not given a perimeter of 36 inches.

Ans. Option 1.

Hope this helps.

You can use the **guess and check method**, in which you take one of the multiple choice answers and see if they work out/compare them to the other answers.

For example, we can try answer choice 3, because of no particular reason, just that it's in the middle of the set of choices and it seems nice that way. The equation for the perimeter of a rectangle is as follows:

`2(l+w)`

With l=length and w=width. When we **plug in,** or enter the values for l and w with choice 3's values, we get

`2(27+9)`

`(2*27)+(2*9)`

`(54)+(18)`

`72`

72 is what we get for answer choice 3. However, that is double the amount that the question gave us for the perimeter of the rectangle. If we keep on using this method, we will finally find that **answer choice 1 is the only choice that satisfies the conditions.**

Hope I helped!

You can also solve this algebraically, or by just thinking in your head; answer choice 1: 9+9, 9+9= 18 and 18 equal 36! This guess and check method does take a while to do, but it is the easiest way to solve this problem if you don't know any other methods.

The perimeter of the rectangle = 2(L + W) = 36

=> L+W =18

on **trail and error methods of the options**

only L=9 , W =9 satisfies the option

so the maximum area is = L * W =9*9 =**81**