Question
The rectangle is 20cm². The length is x+4cm and the width is x-4cm respectively. What is the value of x in centimetres?
Answers
GPT-4o mini
To find the value of \( x \), we start with the area of the rectangle given as:
\[
\text{Area} = \text{Length} \times \text{Width}
\]
Substituting the expressions for length and width:
\[
20 = (x + 4)(x - 4)
\]
We recognize that \( (x + 4)(x - 4) \) is a difference of squares, which simplifies to:
\[
x^2 - 16
\]
Now we can set up the equation:
\[
20 = x^2 - 16
\]
Next, we will add 16 to both sides:
\[
20 + 16 = x^2
\]
This simplifies to:
\[
36 = x^2
\]
To solve for \( x \), we take the square root of both sides:
\[
x = \sqrt{36} \quad \text{or} \quad x = -\sqrt{36}
\]
\[
x = 6 \quad \text{or} \quad x = -6
\]
Since \( x \) represents a length, we discard the negative value. Therefore, the value of \( x \) is:
\[
\boxed{6} \text{ cm}
\]
\[
\text{Area} = \text{Length} \times \text{Width}
\]
Substituting the expressions for length and width:
\[
20 = (x + 4)(x - 4)
\]
We recognize that \( (x + 4)(x - 4) \) is a difference of squares, which simplifies to:
\[
x^2 - 16
\]
Now we can set up the equation:
\[
20 = x^2 - 16
\]
Next, we will add 16 to both sides:
\[
20 + 16 = x^2
\]
This simplifies to:
\[
36 = x^2
\]
To solve for \( x \), we take the square root of both sides:
\[
x = \sqrt{36} \quad \text{or} \quad x = -\sqrt{36}
\]
\[
x = 6 \quad \text{or} \quad x = -6
\]
Since \( x \) represents a length, we discard the negative value. Therefore, the value of \( x \) is:
\[
\boxed{6} \text{ cm}
\]