Question

Find the measure of DF

Answer 1

DF = 50

Explanation:

`\bold{METHOD\ 1:}`

`\triangle ABC\sim\triangle DE F\qquad(\text{similar tringles)}\\\\\text{Therefore corresponding sides are in proportion:}\\\\(BA)/(AC)=(ED)/(DF)\\\\\text{Substitute}\ BA=360,\ AC=600,\ ED=30\\\\(360)/(600)=(30)/(DF)\qquad\text{cross multiply}\\\\360DF=(600)(30)\\\\360DF=18000\qquad\text{divide both sides by 360}\\\\DF=50`

`\bold{METHOD\ 2:}`

`\text{Use the Pythagorean theorem:}\\\\leg^2+leg^2=hypotenuse^2\\\\\text{We have}\ leg=40,\ leg=30,\ hypotenuse=DF.\\\\\text{Substitute:}\\\\40^2+30^2=DF^2\\\\1600+900=DF^2\\\\2500=DF^2\to DF=√(2500)\\\\DF=50`