A rectangular ink pad has an area of 40 square centimetres. Its perimeter is 28 centimetres. What are the dimensions of the ink pad?

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

We are given that A = 40 cm² and P = 28 cm.

Let's start by setting up two equations based on the information given:

1. L * W = 40
2. 2L + 2W = 28

We can simplify the second equation by dividing every term by 2, which gives us:

L + W = 14

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 = 14 - W

Now we can substitute L in the first equation:

(14 - W) * W = 40

This simplifies to:

14W - W² = 40

Rearranging terms gives us a quadratic equation:

W² - 14W + 40 = 0

We can solve this quadratic equation for W using the quadratic formula:

W = [14 ± sqrt((14)² - 4140)] / (2*1) W = [14 ± sqrt(196 - 160)] / 2 W = [14 ± sqrt(36)] / 2 W = [14 ± 6] / 2 W = 8 or W = 4

So, the dimensions of the rectangle are 8 cm and 4 cm.