Keywords:
Rectangle, length, width, area, inches, equation, variable
For this case, we have a ractangle of area 104 square inches, they tell us that its length is 5 inches greater than the width. In addition, we have the following equation [tex](x + 5) x = 104[/tex] where the variable "x" represents the width of the rectangle.
By definition, the area of a rectangle is given by:
[tex]A = l * x[/tex]
Where:
[tex]A = 104[/tex] square inches
For the width we have:
[tex](x + 5) x = 104\\x ^ 2 + 5x = 104\\x ^ 2 + 5x-104 = 0[/tex]
We find the solutions of the equation by factoring, that is, we look for two numbers that when multiplied give as result -104 and when summed give as result +5. So, those numbers are +13 and -8.
[tex]13 * -8 = -104\\13-8 = + 5[/tex]
So, we have:
[tex](x + 13) (x-8) = 0[/tex]
The roots are:
[tex]x_ {1} = - 13\\x_ {2} = 8[/tex]
The solution that makes sense for the width of the rectangle is: x_ {2} = 8
Thus, the width of the rectangle is x = 8 inches
If the thickness is 5 inches greater than the width, then:
[tex]l = 5 + 8\\l = 13\ inches.[/tex]
Verifying the area, we have:
[tex]A = 13 * 8 = 104[/tex] square inches
ANswer:
[tex]width = 8\ inches\\length = 13\ inches[/tex]
