Mathematics, 27.06.2021 02:20, stressedstudent6402

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

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answered: MARTINASLACK299

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:

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

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

$\large{32 = x \times 2x}$

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.

$\large{ \frac{32}{2} = {x}^{2} }$

Simplify 32/2 in simplest form.

$\large{16 = {x}^{2} }$

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

$\large{ \sqrt{16} = \sqrt{ {x}^{2} } }$

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:

$\large \boxed{ \tt{P = (width + length) \times 2}}$

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

$\large{P = (4 + 8) \times 2} \\ \large{P = 12 \times 2} \\ \large \boxed{P = 24}$

Hence, the perimeter is 24.

Answer

The perimeter for the rectangle is 24.

answered: awesome267

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 ..