Geometry/Chapter 4/Lesson 8

• y = Hypothenuse of ${\displaystyle ABD}$
• x = Altitude
• z = Hypothenuse of ${\displaystyle ADC}$

1. ${\displaystyle x=}$ ${\displaystyle {\tfrac {x}{4}}=}$ • ${\displaystyle {\tfrac {7}{x}}}$
2. ${\displaystyle y=}$ ${\displaystyle {\tfrac {y}{4}}=}$ • ${\displaystyle {\tfrac {11}{y}}}$
3. ${\displaystyle z=}$ ${\displaystyle {\tfrac {z}{7}}=}$ • ${\displaystyle {\tfrac {11}{z}}}$

1. ${\displaystyle x=}$ ${\displaystyle {\tfrac {x}{4}}=}$ • ${\displaystyle {\tfrac {7}{x}}}$
2. √${\displaystyle x}$² ${\displaystyle =}$ √${\displaystyle 28}$
3. ${\displaystyle x=}$ ${\displaystyle 2}$√${\displaystyle 7}$

1. ${\displaystyle y=}$ ${\displaystyle {\tfrac {y}{4}}=}$ • ${\displaystyle {\tfrac {11}{y}}}$
2. √${\displaystyle y}$² ${\displaystyle =}$ √${\displaystyle 44}$
3. ${\displaystyle y=2}$√${\displaystyle 11}$

1. ${\displaystyle z=}$ ${\displaystyle {\tfrac {z}{7}}=}$ • ${\displaystyle {\tfrac {11}{z}}}$
2. √${\displaystyle z}$² ${\displaystyle =}$ √${\displaystyle 77}$
3. ${\displaystyle z=}$ √${\displaystyle 77}$

Answer:

• ${\displaystyle x=}$ ${\displaystyle 2}$√${\displaystyle 7}$
• ${\displaystyle y=2}$√${\displaystyle 11}$
• ${\displaystyle z=}$ √${\displaystyle 77}$