Question

The rectangle below has an area of x2 + 11x + 28 square meters and a length of 2 + 7 meters.

Answer 1

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:

$\text {Area of rectangle }=\text { length } \times \text { width }$

Here area = x^2 + 11x + 28 square meters

length = x + 7 meters

Substituting the values in given formula,

$\begin{array}{l}{\text { width }=\frac{x^{2}+11 x+28}{x+7}} \\\\ {\text { width }=\frac{x^{2}+4 x+7 x+28}{x+7}} \\\\ {\text { width }=\frac{x(x+4)+7(x+4)}{x+7}} \\\\ {\text { width }=\frac{(x+4)(x+7)}{x+7}}\end{array}$

Cancelling (x + 7) on numerator and denominator,

$\text { width }=(x+4)$

Thus expression representing width of rectangle is (x + 4) meters