Chapter 2.1, Problem 57E

To determine

An inequality to represent the missing dimension x

Answer to Problem 57E

  $x<3$

Explanation of Solution

Given:

The area is less than 18 square centimeters.

Formula used:

Area of rectangle $=length\times breadth$

Area of triangle $=\frac{1}{2}\times base\times height$

Calculation:

From the figure,

Length of the rectangle $=4$ cm

Breadth of the rectangle $=x$

Base of the triangle $=8-4=4$ cm

Height of the triangle $=x$

Therefore, area of the rectangle $=4\times x=4x$ square cm

And, area of triangle $=\frac{1}{2}\times 4\times x=2x$ square cm

Then, total area of the figure $=$ area of rectangle + area of triangle $=4x+2x=6x$ square cm

It is given, that area is less than 18 square centimeters

Then the inequality is

  $\begin{array}{l}6x<18\\ \Rightarrow x<3\end{array}$

Thus, an inequality to represent the missing dimension xis $x<3$