Two siblings, Sarah and Tom are playing a simultaneous hit and tell game. Sarah can hit Tom or not and Tom can tattle on Sarah or not. Relative to no hitting and no tattling, if Sarah hits Tom, and he tattles they both experience a loss of 10. Not telling, gets Tom a bruise, a loss of 5 but Sarah gains 5. If he tattles untruthfully, he gets a gain of 5 and Sarah loses 5. If they get along, no one gets anything. If Tom tattles, what would Sarah's best response be?

bd = 9 cm

step-by-step explanation:

in a 30°-60°-90° triangle, the ratio of side lengths is 1 : √3 : 2. that is, the longest side (hypotenuse) is twice the length of the shortest side.

all of the triangles in your geometry are 30°-60°-90° triangles. ac is the hypotenuse of δacd, and the short side of δabc.

the short side ad of δacd will be half the length of ac, so 3 cm. the hypotenuse ab of δabc will be twice the length of ac, so 12 cm. segment bd is the difference of the lengths ab and ad, so is

bd = ab -ad

bd = 12 cm - 3 cm = 9 cm

comment on side length ratios

you can figure the ratios of side lengths in a 30°-60°-90° triangle by considering the trig ratios of the angles. or you can figure the length of the altitude of an equilateral triangle of side length 2 using the pythagorean theorem.

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