Chapter 7.6, Problem 38SPR

To determine

Find the value of the given measurement using kite diagram.

Answer to Problem 38SPR

The length of $BC=13$ .

Explanation of Solution

Given:

The given measurement is $BC$ and the given diagram is

  

Calculation:

Diagonals of a kite are perpendicular to each other.

Use Pythagoras theorem.

  $c^2=a^2+b^2$

  $c=$ hypotenuse

  $a=$ perpendicular

  $b=$ base

In the given figure, $a=5,b=12,c=CD$ .

  $\begin{array}{l}{c}^2=5^2+{12}^2\\ \Rightarrow CD=\pm \sqrt{5^2+{12}^2}\\ \Rightarrow CD=\pm \sqrt{169}\\ \Rightarrow CD=\pm 13\end{array}$

Length must be positive.

  $CD=13$

In the diagram $BC=CD$ .

  $\Rightarrow BC=13$

Hence the length of $BC=13$ .