The length of a rectangle is twice its width. If the perimeter of the rectangle is 30 cm , find its area. $$ \left\lfloor\mathrm{cm}^{2}\right. $$

Question

UpStudy AI · Accepted Answer

Let the width be $$ w $$ and the length be $$ 2w $$.

1. The perimeter $$ P $$ of a rectangle is given by:
   $$
   P = 2(w + 2w) = 2(3w) = 6w.
   $$

2. Given that the perimeter is $$ 30 $$ cm, set up the equation:
   $$
   6w = 30.
   $$

3. Solve for $$ w $$:
   $$
   w = \frac{30}{6} = 5 \text{ cm}.
   $$

4. Find the length:
   $$
   \text{Length} = 2w = 2 \times 5 = 10 \text{ cm}.
   $$

5. Calculate the area $$ A $$ of the rectangle:
   $$
   A = \text{width} \times \text{length} = 5 \times 10 = 50 \text{ cm}^2.
   $$

Thus, the area of the rectangle is $$ 50 \text{ cm}^2 $$.
The area of the rectangle is 50 cm².

The length of a rectangle is twice its width. If the perimeter of the rectangle is 30 cm , find its area. \( \left\lfloor\mathrm{cm}^{2}\right. \)