- Perimeter of a rectangle = [tex] 2b+2h [/tex]
- Area of a rectangle = [tex] bh [/tex]
So for this, we will be doing a system of equations, one representing the sum of their areas and the other representing the sum of their perimeters:
[tex] 2x+9y=46\\\\4+2x+18+2y=40\\2x+2y+22=40 [/tex]
So with this, I will be using the elimination method. So firstly, subtract 22 on both sides of the second equation:
[tex] 2x+9y=46\\2x+2y=18 [/tex]
Next, subtract the second equation from the first equation and you should get [tex] 7y=28 [/tex] . From here we can solve for y.
For this, just divide both sides by 7 and your first answer will be y = 4.
Now that we have the value of y, substitute it into either equation to solve for x as such:
[tex] 2x+9*4=46\\2x+36=46\\2x=10\\x=5\\\\2x+2*4=18\\2x+8=18\\2x=10\\x=5 [/tex]
In short, x = 5 and y = 4.
