1) A box has two shapes: 1 triangle, 1 square. Without looking, pull a shape then roll a number cube (a cube has 6 faces). 2) 2. A bag has 3 balls: 1 black, 1 white, 1 red. Without looking, pull a ball and toss a coin (coin has heads and tails).

f bags

Step-by-step explanation: 1. Gbag

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

answer: 4