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.

Hint: label the figure.
x-sin
sin

Answer 1

Use the area of rectangle formula which is:

`\displaystyle \large \tt{A = width * length}`

Given that:

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

Substitute in the formula:

`\displaystyle \large{16 = 8 * (x - 5)} \\ \displaystyle \large{16 = 8(x - 5)}`

Distribute 8 in the expression:

`\displaystyle \large{16 = (8 * x) + (8 * ( - 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{ (56)/(8) = x} \\ \displaystyle \large{7 = x} \\`

Hence, the answer is:

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