The perimeter of a rectangular garage is 40 metres. The area is 75 square metres. What are the dimensions of the garage?

To find the dimensions of the rectangle (length and width), we can use the formulas for the perimeter and area of a rectangle.

The perimeter (P) of a rectangle is given by the formula P = 2L + 2W, where L is the length and W is the width. The area (A) is given by the formula A = LW.

From the problem, we know that P = 40 and A = 75.

We can start by expressing the width (W) in terms of the length (L) using the perimeter formula:

40 = 2L + 2W => 20 = L + W => W = 20 - L

Next, we substitute W = 20 - L into the area formula:

75 = L * (20 - L)

This is a quadratic equation in the variable L. We can solve it by setting it equal to zero:

0 = L^2 - 20L + 75

The solutions to this equation give the possible values for L. We can find these by factoring, completing the square, or using the quadratic formula. In this case, the equation factors to:

0 = (L - 15)(L - 5)

Setting each factor equal to zero gives the solutions L = 15 and L = 5. These are the possible lengths of the rectangle.

Substituting L = 15 into the equation W = 20 - L gives W = 5. Substituting L = 5 gives W = 15.

So the dimensions of the rectangle are 15 metres by 5 metres.