Question

the area of the rectangle below is $x^2 + 13x + 36$ square meters and length $x + 9$ meter. what will be the width of the rectangle? width meter

Explanation:

Step1: Recall the area formula for a rectangle.

The area \( A \) of a rectangle is given by \( A = \text{length} \times \text{width} \). So, if we know the area and the length, we can find the width by \( \text{width} = \frac{\text{area}}{\text{length}} \).

Step2: Identify the area and length.

From the problem, the area of the rectangle is \( x^2 + 13x + 36 \) square meters and the length is \( x + 9 \) meters. So we need to perform the division \( \frac{x^2 + 13x + 36}{x + 9} \).

Step3: Factor the numerator.

We factor the quadratic expression \( x^2 + 13x + 36 \). We need two numbers that multiply to \( 36 \) and add up to \( 13 \). The numbers \( 4 \) and \( 9 \) work because \( 4 \times 9 = 36 \) and \( 4 + 9 = 13 \). So, \( x^2 + 13x + 36 = (x + 4)(x + 9) \).

Step4: Perform the division.

Now we substitute the factored form of the numerator into the division:
\[
\frac{(x + 4)(x + 9)}{x + 9}
\]
Assuming \( x
eq -9 \) (since we can't divide by zero), we can cancel out the common factor \( x + 9 \) from the numerator and the denominator. This leaves us with \( x + 4 \).

Answer:

The width of the rectangle is \( x + 4 \) meters.