If bc = 6 and ad = 5, find dc. a) 4 b) 4.5 c) 7.2

We have three similar triangles, because each has a right angle and shares an angle.   Let's write the angles in order: opposite to short leg, long leg, hypotenuse.

CAB similar to BAD similar to CBD

Or as ratios,

CA:AB:CB = BA:AD:BD = CB:BD:CD

We also know

AC = AD + CD

(AD+CD):AB:CB = BA:AD:BD = CB:BD:CD

(AD+CD)/CB=CB/CD

We have CB=6, AD=5 and seek x=CD.

We reject the negative root and conclude x=4

4

there is no question content here, but you for the free points! : d

your answer would be 12