Question

what will be the width of the rectangle?
length — 7 meter.
width
$x^2 - 15x + 56$
$x - 7$
width
meter

Explanation:

Step1: Recall area formula of rectangle

The area of a rectangle is given by \( A = \text{length} \times \text{width} \). Here, the area is \( x^{2}-15x + 56 \) and the length is \( x - 7 \). Let the width be \( w \), so we have \( x^{2}-15x + 56=(x - 7)\times w \). To find \( w \), we need to divide the area by the length, i.e., \( w=\frac{x^{2}-15x + 56}{x - 7} \).

Step2: Factor the quadratic expression

Factor the numerator \( x^{2}-15x + 56 \). We need two numbers that multiply to \( 56 \) and add up to \( - 15 \). The numbers are \( -7 \) and \( -8 \) because \( (-7)\times(-8)=56 \) and \( (-7)+(-8)=-15 \). So, \( x^{2}-15x + 56=(x - 7)(x - 8) \).

Step3: Divide the factored form by length

Now, substitute the factored form into the division: \( w=\frac{(x - 7)(x - 8)}{x - 7} \). Since \( x
eq7 \) (to avoid division by zero), we can cancel out the common factor \( (x - 7) \) from the numerator and the denominator.

Answer:

The width of the rectangle is \( x - 8 \) meters.