Question

Please help

Find CD.

1.) 4.5

2.) 5.3

3.) 5.5

4.) 6.3

Answer 1

CD = 6.3

Explanation:

triangles CFG and CDE are similar, so their side lengths are proportional

this means CD/CF = CE/CG

since we don't know CF, we need to first solve for CF in order to find CD

luckily, we know CD = CF + FD, and FD is given:

CD/CF = CE/CG -> (CF + FD) / (CF) = CE/CG

multiply both sides by CF to get CF + FD = CE * CF / CG

move the terms with CF to one side, and the constants to the other side:

CF - CF(CE/CG) = -FD

solve for CF:

CF(1-(CE/CG)) = -FD, CF = FD / ((CE/CG) - 1) = (1.8)/(((2.4+6)/(6)) - 1) = 4.5

Since CD = CF+FD, CD = 4.5 + 1.8 = 6.3