A rectangular building has an area of 1512 square metres. Its perimeter is 164 metres. What are the dimensions of the building?

To find the dimensions of the building, we can use the formulas for the area and perimeter of a rectangle.

The area (A) of a rectangle is given by the formula A = length * width. We know that the area is 1512 square metres.

The perimeter (P) of a rectangle is given by the formula P = 2 * (length + width). We know that the perimeter is 164 metres.

Let's denote the length of the rectangle as L and the width as W.

From the area formula, we have:

1. L * W = 1512

From the perimeter formula, we have:

2. 2 * (L + W) = 164 which simplifies to: L + W = 82

Now we have a system of two equations, and we can solve it step by step.

First, let's express L from the second equation:

L = 82 - W

Now we can substitute L from this equation into the first one:

(82 - W) * W = 1512

This is a quadratic equation. Solving it gives us the possible values for W:

W = 36 or W = 46

Substituting these values back into the equation L = 82 - W gives us the corresponding lengths:

L = 46 or L = 36

So, the dimensions of the building are 36 metres by 46 metres.