Chapter 9.6, Problem 10PSA

To determine

To Calculate: The length of QD

Answer to Problem 10PSA

The length of QD is $17$

Explanation of Solution

Given information:

Measures of lengths

AD = $9$

AU = $12$

QU = $8$

Formula used:

Here, we are using Pythagoras theorem.

  ${\left(base\right)}^2={\left(perpendicular\right)}^2-{\left(hypotenuse\right)}^2$

Calculation:

Here, the formula is

  ${\left(base\right)}^2={\left(perpendicular\right)}^2-{\left(hypotenuse\right)}^2$

  ${\left(UD\right)}^2={\left(UA\right)}^2+{\left(AD\right)}^2$

  ${\left(UD\right)}^2=144+81$

  ${\left(UD\right)}^2=225$

  $UD=15$

And, ${\left(QD\right)}^2={\left(UQ\right)}^2+{\left(UD\right)}^2$

  ${\left(QD\right)}^2=64+225$

  $QD=17$

Conclusion: Hence,the length of QD is $17$