Chapter 9.3, Problem 1PSA

a

To determine

To find:The value of segment HF

Answer to Problem 1PSA

The value of $HF=\sqrt{21}$

Explanation of Solution

Given information:The following information has been given

  $EH=7$

  $HG=3$

Formula used:The ratio of sides is same for similar triangles

Calculation:We know that in similar triangles HFE and HGF,

  $\frac{HF}{HG}=\frac{FE}{GF}=\frac{HE}{HF}$ (by law of similarity)

Hence, we substitute the values of EH and HG in the equation above, we get

  $H{F}^2=HE(HG)$

Thus, we get

  $HF=\sqrt{21}$

b

To determine

To find:The value of segment EF

Answer to Problem 1PSA

The value of $FE=\sqrt{77}$

Explanation of Solution

Given information:The following information has been given

  $EH=7$

  $HG=4$

Formula used:Similar triangles have sides in same ratio.

Calculation:We know that in similar triangles HFE and FGE,

  $\frac{HF}{FG}=\frac{FE}{GE}=\frac{HE}{FE}$ (by law of similarity)

Hence, we substitute the values of EH and HG in the e equation above, we get

  $F{E}^2=HE(GE)$

Thus, we get

  $FE=\sqrt{77}$

c

To determine

To find:The value of segment HG.

Answer to Problem 1PSA

The value of $GF=3\sqrt{6}$

Explanation of Solution

Given information:The following information has been given

  $GF=6$

  $EG=9$

Calculation:We know that in similar triangles FGE and HGF,

  $\frac{FG}{HG}=\frac{GE}{GF}=\frac{FE}{HF}$ (by law of similarity)

Hence, we substitute the values of EH and HG in the equation above, we get

  $G{F}^2=GE(HG)$

Thus, we get

  $GF=3\sqrt{6}$