Chapter 1.5, Problem 22WE

To determine

To write: an equation involving x , when given area of the rectangle in given figure with length x , and width $\left(x+1\right)$ is 42.

Answer to Problem 22WE

  $x^2+x=42$

Explanation of Solution

Given:

  

Concept Used:

Area of a rectangle is product of it’s length and width. That is, area of a rectangle with length a , and width b is given by: $a\times b$ .

Calculation:

In order to write an equation involving x , when given area of the rectangle in given figure with length x , and breadth $\left(x+1\right)$ is 42.

Since, area of a rectangle is product of it’s length and width.

Here, width is $\left(x+1\right)$ , length is x , and area is 42.

Thus, from the given information

  $\begin{array}{c}\left(x+1\right)\times x=42\\ \Rightarrow x\left(x+1\right)=42\\ \Rightarrow x\cdot x+x=42;\text{ distributive property}\\ \Rightarrow x^2+x=42\end{array}$

Thus, the equation formed from the given information involving x is:

  $x^2+x=42$