Question

the area of the rectangle below is $x^2 - 11x + 30$ square length $x - 5$ meter.
what will be the width of the rectangle?
$x - 5$
width
$x^2 - 11x + 30$
width
meter

Explanation:

Step1: Recall the formula for the area of a rectangle

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

Step2: Substitute the given area and length into the formula

We know the area \( A = x^2 - 11x + 30 \) and the length \( l = x - 5 \). So, we need to perform the division \( \frac{x^2 - 11x + 30}{x - 5} \).

Step3: Factor the quadratic expression in the numerator

We factor \( x^2 - 11x + 30 \). We need two numbers that multiply to 30 and add up to -11. Those numbers are -5 and -6. So, \( x^2 - 11x + 30 = (x - 5)(x - 6) \).

Step4: Simplify the fraction

Now, substitute the factored form into the division: \( \frac{(x - 5)(x - 6)}{x - 5} \). We can cancel out the common factor \( x - 5 \) (assuming \( x
eq 5 \), which is valid because if \( x = 5 \), the length would be 0, which doesn't make sense for a rectangle). So, we are left with \( x - 6 \).

Answer:

The width of the rectangle is \( x - 6 \) meters.