Question

"Bethan builds a new rectangular sheep pen. The perimeter fence of the new sheep pen is 16 m long. The length of the new sheep pen is 3 metres longer than the width. Form an equation and solve it to find the dimensions of this new sheep pen."

Can someone explain how to do it? Like I have the answer and it's right, but how do I it? :')
FYI answer is:
Length = 5.5m
Width = 2.5m ​

Answer 1

To find the dimensions of the new sheep pen, we can set up and solve an equation. The width of the pen can be represented as 'w', and the length is 3 meters longer than the width. By setting up an equation and solving it, we find that the dimensions of the pen are Length = 5.5m and Width = 2.5m.

Step-by-step explanation:

To find the dimensions of the new sheep pen, we can set up an equation using the given information. Let's call the width of the pen 'w'. The length of the pen is 3 meters longer than the width, so it can be represented as 'w + 3'. The perimeter of a rectangle is found by adding up all four sides, so the equation can be written as:

2(w + w + 3) = 16

Simplifying this equation gives:

4w + 6 = 16

Subtracting 6 from both sides gives:

4w = 10

Dividing both sides by 4 gives:

w = 2.5

Therefore, the width of the sheep pen is 2.5 meters. To find the length, we can substitute this value back into the equation:

Length = w + 3 = 2.5 + 3 = 5.5

Therefore, the dimensions of the new sheep pen are Length = 5.5m and Width = 2.5m.