Let's call the width of our rectangle [tex]w[/tex] and the length [tex]l[/tex]. We can say [tex]l = w + 4[/tex], since the length is equal to 4 cm greater than the width.
Also remember that the perimeter of a rectangle is the sum of two times the width and two times the length, or [tex]P = 2l + 2w[/tex]. To solve this problem, we can substitute in the information we know, as shown below:
[tex]150 = 2(w + 4) + 2w[/tex]
[tex]150 = 4w + 8[/tex]
[tex]142 = 4w[/tex]
[tex]w = \frac{71}{2}[/tex]
Now, we can substitute in the width we found into the formula for length, which is [tex]l = w + 4[/tex]:
[tex]l = \frac{71}{2} + 4[/tex]
[tex]l = \frac{79}{2}[/tex]
The width of our rectangle is [tex]\boxed{\frac{71}{2} \,\, \textrm{cm}}[/tex] cm and the length of our rectangle is [tex]\boxed{\frac{79}{2} \,\, \textrm{cm}}[/tex]
