Use the area of rectangle formula which is:
[tex] \displaystyle \large \tt{A = width \times length}[/tex]
Given that:
- area of rectangle = 16
- width = 8
- length = x-5
Substitute in the formula:
[tex] \displaystyle \large{16 = 8 \times (x - 5)} \\ \displaystyle \large{16 = 8(x - 5)}[/tex]
Distribute 8 in the expression:
[tex] \displaystyle \large{16 = (8 \times x) + (8 \times ( - 5))} \\ \displaystyle \large{16 = 8x - 40}[/tex]
Move -40 to another side and change from -40 to 40.
[tex] \displaystyle \large{16 + 40 = 8x} \\ \displaystyle \large{56= 8x} \\ [/tex]
Then move 8 to divide 56, leaving only x.
[tex] \displaystyle \large{ \frac{56}{8} = x} \\ \displaystyle \large{7 = x} \\ [/tex]
Hence, the answer is:
[tex] \displaystyle \large \boxed{x = 7} \\ [/tex]
