Respuesta :
Question:
The rectangle below has an Área of x^2 + 11x + 28 square meters and a length of x+7 meters. What expression represents the width of the rectangle?
Answer:
The expression representing width of rectangle is (x + 4) meters
Solution:
Given that rectangle has an area x^2 + 11x + 28 square meters and a length of x + 7 meters
To find: width of the rectangle
The area of rectangle is given as:
[tex]\text {Area of rectangle }=\text { length } \times \text { width }[/tex]
Here area = x^2 + 11x + 28 square meters
length = x + 7 meters
Substituting the values in given formula,
[tex]\begin{array}{l}{\text { width }=\frac{x^{2}+11 x+28}{x+7}} \\\\ {\text { width }=\frac{x^{2}+4 x+7 x+28}{x+7}} \\\\ {\text { width }=\frac{x(x+4)+7(x+4)}{x+7}} \\\\ {\text { width }=\frac{(x+4)(x+7)}{x+7}}\end{array}[/tex]
Cancelling (x + 7) on numerator and denominator,
[tex]\text { width }=(x+4)[/tex]
Thus expression representing width of rectangle is (x + 4) meters
