Chapter 14, Problem 6CTE

To determine

To construct: any triangle of area $xy$ with $x>y$ , where $x,y$ are two line segment.

Answer to Problem 6CTE

  

Explanation of Solution

Given information:

Instructed to consider two line segment $x,y,x>y$ and find a triangle of area $xy$ .

Calculation:

Let us take $x=3cm.,y=4cm.$ So that the area of the triangle must be $12cm{.}^2$

The area of a triangle is $\frac{1}{2}\times base\times height$ . Now,

  $\begin{array}{l}\frac{1}{2}\times base\times height=xy=12\\ \Rightarrow base\times height=24=(3\times 8)\text{ or (4}\times \text{6) etc}\end{array}$

So we have to make a triangle of base $\text{8cm}\text{.}$ and height $\text{3cm}\text{.}$ so that its area become $12cm{.}^2$ as below.

  

Hence the triangle is formed.