Question

Say EG = 2 and EF = 8, find the length of segment ED.

Answer 1

this is all about proportions

we are given that \(\overline{EG} = 2 \ \ \ \vee \ \ \ \overline{EF} = 8\)

first lets find \( \overline{GF} \ \ \ | \ \ \ \overline{GF} = \overline{EF} - \overline{GF} = 8-2=6 \ units\)

these are similar triangles right,so all the sides are proportional, which means we can set a proportion:

\( \frac{ \overline{GD}}{ \overline{EG}}=\frac{ \overline{GF}}{ \overline{GD}} \)

\( \frac{ \overline{GD}}{2}=\frac{ 6}{ \overline{GD}} \)

\( (\overline{GD} )^2 = 12 \implies \ \overline{GD} = \sqrt{12 } \)

so we have this right triangle as drawn


Can you find C?