Chapter 5.5, Problem 11PSA

To determine

To find: Thevalue of $KT$ which is one of the diagonals of a kite.

Answer to Problem 11PSA

The value of $KT$ is 240.

Explanation of Solution

Given Information:

  $KI=IT\text{and}KE=ET$

  $KP=6x$

  $\angle IPT={\left(5x-10\right)}^{\text{o}}$

Formula used:

The diagonals of a kite bisect and perpendicular to each other.

Calculation:

Here, $KITE$ is a kite and we know that the diagonals of a kite bisect and perpendicular to each other.

  $\Rightarrow KP=PT\text{and}\angle IPT={90}^{\text{o}}$

As $KP=6x$ and $\angle IPT={\left(5x-10\right)}^{\text{o}}$

  $\Rightarrow KT=KP+PT=12x$ and $5x-10=90$

  $\begin{array}{l}\Rightarrow 5x=100\\ \Rightarrow x=20\end{array}$

  $\begin{array}{l}\Rightarrow KT=12\times 20\\ \Rightarrow KT=240\end{array}$

Hence, the value of $KT$ is 240.