Question

The length of a rectangle is twice its width. If the area of the rectangle is

32cm2, find the perimeter.​

Answer 1

after you list the factors, you have to read the question back .. the question the length of the rectangle is twice the width .. so 4 × 8 is the correct answer .. and you do as usual to calculate the perimeter ..

Answer 2

Before we find the perimeter, first we must know length and width.

Let width = x

The question says that the length of a rectangle is twice its width. Therefore the length is 2×x or two times of width which equal to 2x.

The area of rectangle is given as 32 cm^2.

Do you remember the rectangle area formula? If not then it is:

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

Since A is area - substitute A = 32 in. As for width, we substitute in x and length in 2x.

`\large{32 = x * 2x}`

Since x multiplies by another x. It becomes x squared.

`\large{32 = 2{x}^(2) }`

Next, we divide 2 by both sides since we want to solve for x.

`\large{ (32)/(2) = {x}^(2) }`

Simplify 32/2 in simplest form.

`\large{16 = {x}^(2) }`

Square both sides so we can get rid the x squared, leaving only x.

`\large{ √(16) = \sqrt{ {x}^(2) } }`

Normally, when solving quadratic equation, you must write plus or minus. However, for this circumstance - we are solving a variable for length and width which cannot be negative. Therefore

`\large{4 = x}`

After we solve for x. Substitute x = 4 in width = x and length = 2x.

`\large{ \tt{width = x = 4}} \\ \large{ \tt{length = 2x = 2(4) = 8}}`

When we multiply these two numbers, we get 32 cm^2.

Next, we find the perimeter. The formula of perimeter for rectangle is:

`\large \boxed{ \tt{P = (width + length) * 2}}`

We know width and length which are 4 and 8 in order. Substitute in the formula.

`\large{P = (4 + 8) * 2} \\ \large{P = 12 * 2} \\ \large \boxed{P = 24}`

Hence, the perimeter is 24.

Answer

• The perimeter for the rectangle is 24.