The area of square ABCD is 10 cm² - Edexcel - GCSE Maths - Question 4 - 2017 - Paper 1

To show this, we start by using the formula for the area of a square, which is given by:

$ext{Area} = ext{side}^2$

In this case, the side of the square ABCD is given as the sum of its parts:

$ext{side} = 3 ext{ cm} + x ext{ cm} = (3 + x) ext{ cm}$

Thus, the area can also be expressed as:

$(3 + x)^2 = 10$

Next, we expand this expression:

$(3 + x)^2 = 9 + 6x + x^2$

Now we set this equal to the area:

$9 + 6x + x^2 = 10$

Rearranging the equation gives:

$x^2 + 6x + 9 - 10 = 0$

This simplifies to:

$x^2 + 6x - 1 = 0$

The task now is to isolate the expression on one side of the equation. We can do that by adding 1 to both sides to get:

$x^2 + 6x = 1$

Thus, we have shown that the equation $x^2 + 6x = 1$ holds true.