For this case we have that by definition, the area of a rectangle is given by:
[tex]A = a * b[/tex]
Where:
a: It is the length of the rectangle
b: It is the width of the rectangle
We have as data:
[tex]A = 24\\a = A\\b = A-5[/tex]
So:
[tex]A (A-5) = 24\\A ^ 2-5A = 24\\A ^ 2-5A-24 = 0[/tex]
We look for two numbers that when multiplied get -24 and when added get -5.
These numbers are -8 and 3:
[tex](A-8) (A + 3) = 0[/tex]
Thus, the solutions are:
[tex]A_ {1} = 8\\A_ {2} = - 3[/tex]
We choose the positive value, so the length of the rectangle is A = 8
Answer:
8 centimeters
