Question

 The rectangle has an area of 24 square centimeters. Find the length a of the rectangle.

Answer 1

For this case we have that by definition, the area of a rectangle is given by:

$A = a * b$

Where:

a: It is the length of the rectangle

b: It is the width of the rectangle

We have as data:

$A = 24\\a = A\\b = A-5$

So:

$A (A-5) = 24\\A ^ 2-5A = 24\\A ^ 2-5A-24 = 0$

We look for two numbers that when multiplied get -24 and when added get -5.

These numbers are -8 and 3:

$(A-8) (A + 3) = 0$

Thus, the solutions are:

$A_ {1} = 8\\A_ {2} = - 3$

We choose the positive value, so the length of the rectangle is A = 8

Answer:

8 centimeters