We are given that P = 2l + 2w, P = 24, l = w + 3.
Now, just substitute the information into the formula:
[tex]24 = 2(w+3) + 2(w)[/tex]
Now, just solve for w:
[tex]24 = 4w + 6[/tex]
[tex]18 = 4w[/tex][tex]w = \frac{18}{4} [/tex]
Now that we have the value for w, plug it back in to the equation l = w + 3
[tex]l = w + 3[/tex]
[tex]l = \frac{18}{4}+3
[/tex]
[tex]l = \frac{30}{4} [/tex]
Now, just simplify the fractions: 18/4 = 9/2; 30/4 = 15/2
The width of the rectangle is 9/4. The height of the rectangle is 15/2. Hope this helps and have a significant day!
