Question

the hypotenuse of a right triangle is 12 centimeters, and the shorter leg is 6 centimeters. find the length of the other leg. user: a person has 17 coins, all quarters and dimes, worth $3.05. how many quarters are there?

Answer 1

a^2 + b^2 = c^2....a and b are the legs and c is the hypotenuse
6^2 + b^2 = 12^2
36 + b^2 = 144
b^2 = 144 - 36
b^2 = 108
b = sqrt 108
b = 10.39 cm <== length of the other leg

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q + d = 17....d = 17 - q
0.25q + 0.10d = 3.05

0.25q + 0.10(17 - q) = 3.05
0.25q + 1.7 - 0.10q = 3.05
0.25q - 0.10q = 3.05 - 1.7
0.15q = 1.35
q = 1.35/0.15
q = 9 <=== there is 9 quarters