The length of a rectangle is twice its width. If the area of the rectangle is 32cm2, find the perimeter.​

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:

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

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

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

Simplify 32/2 in simplest form.

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

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

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

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

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

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

Hence, the perimeter is 24.

Answer

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 ..

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step-by-step explanation: