SOLUTION: What is the height of an equilateral triangle with sides that are 12 cm long? Round to the nearest tenth. a. 6 cm b. 10.4 cm c. 8.5 cm d. 6.9 cm A courtyard is shaped

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Question 948931: What is the height of an equilateral triangle with sides that are 12 cm long? Round to the nearest tenth.
a. 6 cm b. 10.4 cm c. 8.5 cm d. 6.9 cm
A courtyard is shaped like a square with 250-ft-long sides. What is the distance from one corner of the courtyard to the opposite corner? Round to the nearest tenth.
a. 353.6 ft b. 500 ft c. 433 ft d. 176.8 ft

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
A.) The height of an equilateral triangle forms a right triangle with one side as the hypotenuse and half of one side as a leg. The height is the other leg, so
a is 1/2 length of side =1/2(12 cm)=6cm
b is the height b=h
c is the hypotenuse, one of the sides=12cm
+a%5E2%2Bb%5E2=c%5E2,
%286+cm%29%5E2%2Bh%5E2=%2812+cm%29%5E2
36+sq+cm+%2B+h%5E2=144+sq+cm subtract 36 sq cm from each side.
h%5E2=108+cm Find square root of each side.
h=10.4 cm ANSWER: The height is 10.4 cm. Answer B is correct.
B.) s=length of side; d=diagonal
d=sqrt%282%29s
d=sqrt%282%29%28250+ft%29
d=1.414%28250+ft%29
d=353.6 feet ANSWER: The length of the diagonal is 353.6 feet. Answer A is correct.