A rectangular garage has a perimeter of 28 metres and an area of 40 square metres. What are the dimensions of the garage?

To find the dimensions of the garage, we need to solve for length and width. We know that the perimeter (P) of a rectangle is given by the formula P = 2L + 2W (where L is length and W is width) and the area (A) is given by the formula A = LW.

From the problem, we know that P = 28 and A = 40.

Let's start with the perimeter equation:

28 = 2L + 2W Divide through by 2 to simplify: 14 = L + W (equation 1)

Now let's use the area equation:

40 = LW (equation 2)

We now have a system of two equations. We can solve this system by substitution or elimination. Let's use substitution:

From equation 1, we can express L as L = 14 - W

Substitute L in equation 2:

40 = (14 - W) * W Expand the equation: 40 = 14W - W^2 Rearrange the equation to a standard quadratic form: W^2 - 14W + 40 = 0

Now we can solve this quadratic equation for W. The solutions of the quadratic equation ax^2 + bx + c = 0 are given by the formula:

W = [-(-14) ± sqrt((-14)^2 - 4140)] / (2*1) W = [14 ± sqrt(196 - 160)] / 2 W = [14 ± sqrt(36)] / 2 W = [14 ± 6] / 2 So the solutions are W = 10 and W = 4

Substitute W = 10 and W = 4 into equation 1 to find the corresponding lengths:

When W = 10, L = 14 - 10 = 4 When W = 4, L = 14 - 4 = 10

So the dimensions of the garage are 4 metres by 10 metres.