Chapter 9.5, Problem 18PSB

To determine

To calculate: The Sum of length of two diagonals.

Answer to Problem 18PSB

The Sum of diagonals is $20$ units.

Explanation of Solution

Given information:Here, we have given that vertices are $(0,0)$ , $(8,0)$ , $(0,6)$ and $(8,6)$ .

Formula used: Diagonal of rectangle = $\sqrt{l^2+b^2}$

Distance formula: d = $\sqrt{{(x_2-x_1)}^2+(y_2-y_1)}$ .

Calculation: Let points be A $(0,0)$ , B $(8,0)$ , $(0,6)$ and $(8,6)$ .

so, length AB = $\sqrt{{(8-0)}^2+{(0-0)}^2}$

  $\begin{array}{l}\Rightarrow \sqrt{{(8)}^2}\\ \Rightarrow 8\end{array}$

Similarly, Breadth AC = $\Rightarrow \sqrt{{(0-0)}^2+{(0-6)}^2}$

  $\begin{array}{l}\Rightarrow \sqrt{{(-6)}^2}\\ \Rightarrow \sqrt{36}\\ \Rightarrow 6\end{array}$

Now, Diagonal ( BC )= $\sqrt{l^2+b^2}$

  $\begin{array}{l}\Rightarrow \sqrt{{(8)}^2+{(6)}^2}\\ \Rightarrow \sqrt{64+36}\\ \Rightarrow \sqrt{100}\\ \Rightarrow 10\end{array}$

As, diagonals of rectangle are equal.

  $\Rightarrow$ AD = $10$

  $\therefore$ Sum of diagonals = $10+10=20$