Recall that perimeter of a rectangle can be expressed by 2l + 2w = p, in which l is the length and w is the width.
If the perimeter of a rectangle is 24 inches, we can plug that into the equation and we get the following:
2l + 2w = 24
Now, using the other bit of info, that the length is twice the width, we can create a second equation:
l = 2w
Now, we can plug in l into our value for 2w in our original equation using substitution.
2l + l = 24
By combining like terms, we get this:
3l = 24
Now if we divide both sides by 3, we get that the length equals 8.
Now we can plug 8 into our original equation in place of l.
2(8) + 2w =24
16 + 2w = 24
Subtract 16 from both side:
2w=8
Divide both sides by 2:
w=4
Now we have both the length and the width! We also know that the values are correct because 8, the length, is two times 4, the width.
Now we need to multiply these together to get the area.
8 x 4 = 32
And there you have it! 32 square units is the area.
