Question 7

We will set up an equation using the given information about the rectangle's dimensions and perimeter.

Step 1 — Define variables and form equation

Let's assume the width of the rectangle is $x$ cm. The length is three more than twice its width. So, the length is $2x + 3$ cm. The perimeter of a rectangle is $2 \times (\text{length} + \text{width})$. We are given that the perimeter is 24 cm.

$2((2x + 3) + x) = 24$

$2(3x + 3) = 24$

$6x + 6 = 24$

$6x = 24 - 6$

$6x = 18$

$x = \frac{18}{6}$

$\boxed{x = 3 \text{ cm}}$

Step 2 — Calculate dimensions

Now we know the value of $x$. We can find the width and the length. The width is $x$.

$\text{Width} = 3 \text{ cm}$

The length is $2x + 3$.

$\text{Length} = 2(3) + 3$

$= 6 + 3$

$\boxed{\text{Length} = 9 \text{ cm}}$

Answer

(i) The width of the rectangle is 3 cm. (ii) The length of the rectangle is 9 cm.