Question

If a rectangle has a perimeter of 70, a length of x and a width of x - 9, find the value of the length of the rectangle.

13
31
22
4

Answer 1

The perimeter \( P \) of a rectangle is given by the formula:

\[
P = 2(\text{length} + \text{width})
\]

Let the length be \( x \) and the width be \( x - 9 \). Given that the perimeter is 70, we can set up the equation:

\[
2(x + (x - 9)) = 70
\]

Simplifying the equation:

\[
2(2x - 9) = 70
\]

Dividing both sides by 2:

\[
2x - 9 = 35
\]

Now, add 9 to both sides:

\[
2x = 44
\]

Dividing by 2:

\[
x = 22
\]

Thus, the length of the rectangle is \( \boxed{22} \).