Question

The perimeter of a rectangle is 36 inches, and its length is twice its width. What is the area of the rectangle?​

Answer 1

72 square inches

Explanation:

Given:

Perimeter of rectangle = 36 inches

To find:

Area of the rectangle = ?

Solution:

Let the width of the rectangle be w.

Since the length is twice the width, the length is 2w.

The perimeter of the rectangle is the sum of all four sides. So, we have:

`\sf Perimeter = 2 (length + width)`

Now, substitute the value:

`\sf 36 = 2(2w+w)`

Simplify like terms:

`\sf 36 = 2(3w)`

Distribute the bracket:

`\sf 36 = 2* 3w`

`\sf 36 = 6 w`

Divide by 6 on both sides:

`\sf (36)/(6)=(6w)/(6)`

`\sf 6 = w`

Therefore, width(w)= 6 inches and

Length(2w)= 2 × 6 = 12 inches.

Since, the area of the rectangle is the length times the width.

So, we have:

`\sf Area = Length * width`

Substitute the value:

`\sf Area = 12 inches * 6 inches`

Simplify:

`\sf Area = 72 square inches`

Therefore, the area of the rectangle is 72 square inches.

Answer 2

SEE BELOW ↓

Explanation:

Let's call the width of the rectangle "w" inches. Since the length is twice the width, the length would be "2w" inches.

The formula for the perimeter of a rectangle is

• P = 2(length + width).

Given that, the perimeter is 36 inches, we can write:

• 36 = 2(2w + w)

Now, let's solve for w:

• 36 = 2(3w)

Divide both sides by 2:

• 18 = 3w

Now, divide by 3 to find the width (w):

• w = 18 / 3
• w = 6 inches

So, the width of the rectangle is 6 inches, and the length is 2w = 2 * 6 = 12 inches.

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To find the area of the rectangle, We use the formula:

• Area = length × width

Area = 12 inches × 6 inches = 72 square inches.

Therefore, the area of the rectangle is 72 square inches.