Question

If BC = 6 and AD = 5, find DC. A) 4 B) 4.5 C) 7.2

Answer 1

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.

$(5 + x)/6 = 6/x$

$x(x+5) = 36$

$x^2 +5x - 36 = 0$

$(x+9)(x-4) = 0$

We reject the negative root and conclude x=4

Answer: 4