Chapter 9.5, Problem 21PSB

To determine

To calculate: The Altitude of trapezoid.

Answer to Problem 21PSB

Altitude of trapezoid is $40$ units.

Explanation of Solution

Given information:Here, we have given that length of sides of trapezoid are $2$ , $41$ , $20$ and $41$ .

Formula used: Pythagoras Theorem: ${(P)}^2+{(B)}^2={(H)}^2$

Where

“ P ” is perpendicular

“ B ” is base of the triangle

“ H ” is the hypotenuse of the triangle

Calculation: Let sides be AB = $2$ , AC = $41$ , CD = $20$ and BD = $41$ .

Draw perpendiculars from A and C meeting E and F on CD .

As, AB = $2$ ,

  $\Rightarrow$ EF = $2$

  $\therefore$ CE = DF = $9$

Now, in $\Delta ACE$ ,

  $A{C}^2=A{E}^2+C{E}^2$ (By Pythagoras theorem)

  $\begin{array}{l}$ \Rightarrow {(41)}^2=A{E}^2+{(9)}^2$\Rightarrow 1681=A{E}^2+81\\ \Rightarrow A{E}^2=1681-81\\ \Rightarrow A{E}^2=1600\\ \Rightarrow AE=\sqrt{1600}\\ \Rightarrow AE=40\end{array}$

  $\therefore$ Height = $40$