The length of a rectangle is three centimeters more than twice the width. the perimeter is 78 centimeters. define a variable and write and solve an equation to find out how long and wide the rectangle is?

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

=

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

=

12 = w

w= 12

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

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