Question

A pigpen is marked off so that it’s width is one half of the length.If 4m was subtracted from the length and 24m was added to the width the pigpen would be square. Find the dimensions of the pigpen.

Answer 1

To find the dimensions of the pigpen, use the given equations and solve for the length and width. The dimensions of the pigpen are length = 56m and width = 28m.

Step-by-step explanation:

To find the dimensions of the pigpen, let's represent the length as x and the width as y. According to the problem, the width is one half of the length, so we can write the equation y = x/2. If 4m is subtracted from the length and 24m is added to the width, the pigpen becomes a square. The side length of a square is equal to its width, so we can write the equation (x - 4) = (y + 24).

1. Substitute the value of y from the first equation into the second equation: (x - 4) = (x/2 + 24)
2. Distribute and simplify the second equation: x - 4 = (x + 48)/2
3. Multiply both sides of the equation by 2 to eliminate the fraction: 2(x - 4) = x + 48
4. Distribute and simplify the equation further: 2x - 8 = x + 48
5. Subtract x from both sides of the equation: 2x - x - 8 = 48
6. Combine like terms: x - 8 = 48
7. Add 8 to both sides of the equation: x = 56

Now that we have the value of x, we can substitute it back into the first equation to find the value of y: y = 56/2 = 28.

Therefore, the dimensions of the pigpen are length = 56m and width = 28m.