## Answer :

**Answer:**

The rectangle is **27 centimetres long** and **12 centimetres wide**.

**Step-by-step explanation:**

To solve this problem, we need to follow the steps below;

First, we need to write down the question in a mathematical form.

Let l equal to the length of the rectangle and w equal to the width of the rectangle;

From the question; "The length of a rectangle is three centimetres more than twice the width" can be written down mathematically as

l = 3 + 2w ----------------------------------------------(1)

The question state that the perimeter is 78 centimetres.

Now the formula for calculating the perimeter of a rectangle is

perimeter = 2l + 2w

If the perimeter is 78 centimetres, this implies that;

2l + 2w = 78 ----------------------------------------------(2)

Equation (1) can be rearranged as;

l - 2w = 3 ---------------------------------------------------(3)

We can now solve equation (2) and (3) simultaneously

Add equation (2) and equation (3) together

3l = 81

Divide both-side of the equation by 3

[tex]\frac{3l}{3}[/tex] = [tex]\frac{81}{3}[/tex]

l = 27

substitute l=27 into equation(1)

l = 3 + 2w

27 = 3 + 2w

subtract 3 from both-side of the equation

27 - 3 = 3-3 + 2w

24 = 2w

Divide both-side of the equation by 2

[tex]\frac{24}{2}[/tex] = [tex]\frac{2w}{2}[/tex]

12 = w

w= 12

Therefore, the rectangle is **27 centimetres long** and **12 centimetres wide**.

For a **rectangle **whose **perimeter **is 78 cm, and its *length is three cm more than twice the width*, the **equation **we can derive after defining the *variables *is:

[tex]\mathbf{2[(2w + 3) + w] = 78}[/tex]

[tex]\mathbf{length = 27 $ cm}\\[/tex]

[tex]\mathbf{width = 12 $ cm}\\[/tex]

__Recall:__

**Perimeter **of a **rectangle **= [tex]2(l + w)[/tex], where l is length and w is width.

__Given:__

length of **rectangle**, l, is 3 cm more than 2 times the width, w.

*Thus,*

- length = (2w + 3) cm
- width = w
**Perimeter**= 78 cm

**Equation*** that models this would be:*

[tex]\mathbf{2[(2w + 3) + w] = 78}[/tex]

- Open bracket

[tex]2(2w + 3 + w) = 78\\\\2(3w + 3) = 78\\\\6w + 6 = 78\\\\6w = 78 - 6\\\\6w = 72\\\\\mathbf{w = 12}[/tex]

*The width (w) = 12 cm*

Length = (2w + 3) cm

Plug in the value of w

[tex]Length = 2(12) + 3\\\\\mathbf{Length = 27 $ cm}[/tex]

Therefore, for a **rectangle **whose **perimeter **is 78 cm, and its *length is three cm more than twice the width*, the **equation **we can derive after defining the *variables *is:

[tex]\mathbf{2[(2w + 3) + w] = 78}[/tex]

[tex]\mathbf{length = 27 $ cm}\\[/tex]

[tex]\mathbf{width = 12 $ cm}\\[/tex]

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https://brainly.com/question/18869010