Chapter 9.4, Problem 7PSA

To determine

To Calculate: Themissing length of the trapezoid

Answer to Problem 7PSA

Themissing length of the trapezoid is $10$

Explanation of Solution

Given information:The measures of the given lengths are as follows:

ED = $13$

BC = $7$

FB = $9$

AF = $6$

DC = $8$

Formula used:Here, we are using Pythagoras theorem

  ${\left(Hypotenuse\right)}^2={\left(Perpendicular\right)}^2+{\left(Base\right)}^2$

Calculation:

  

Here, In $\Delta ABE$

  $EB\perp DC$ (by construction) and $BF=9$

Hence, the formula is

  ${\left(Hypotenuse\right)}^2={\left(perpendicular\right)}^2+{\left(base\right)}^2$

In $\Delta ABE$

  ${\left(AB\right)}^2={\left(AE\right)}^2+{\left(EB\right)}^2$

  →${\left(AB\right)}^2={\left(6\right)}^2+{\left(8\right)}^2$

  →${\left(AB\right)}^2=36+64$

  →${\left(AB\right)}^2=100$

  →$AB=10$

Conclusion: Hence,the missing length in the trapezoid is $10$