Question

11. The rectangle has a width of 8 in, a length of x-5 in, and an area of 16 in). Solve for x.

Answer 1

Use the area of rectangle formula which is:

$\displaystyle \large \tt{A = width \times length}$

Given that:

• area of rectangle = 16
• width = 8
• length = x-5

Substitute in the formula:

$\displaystyle \large{16 = 8 \times (x - 5)} \\ \displaystyle \large{16 = 8(x - 5)}$

Distribute 8 in the expression:

$\displaystyle \large{16 = (8 \times x) + (8 \times ( - 5))} \\ \displaystyle \large{16 = 8x - 40}$

Move -40 to another side and change from -40 to 40.

$\displaystyle \large{16 + 40 = 8x} \\ \displaystyle \large{56= 8x}$

Then move 8 to divide 56, leaving only x.

$\displaystyle \large{ \frac{56}{8} = x} \\ \displaystyle \large{7 = x}$

Hence, the answer is:

$\displaystyle \large \boxed{x = 7}$