What is the ratio of the measures of side Modifying Above B C with bar to side Modifying Above Upper R Upper S with bar in simplest form?
Triangle RST is shown with side RS labeled 12 meters, side ST labeled 13 meters, and side TR labeled 5 meters. Triangle BCD is shown with side BC labeled 6 meters, side CD labeled 6.5 meters, and side DB labeled 2.5 meters.
2:1
6:12
1:2
none of these
To find the ratio of the measures of side BC to side RS, we need to determine the lengths of the corresponding sides.
In triangle RST, we can use the Pythagorean theorem to find the length of side RS. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Applying the Pythagorean theorem to triangle RST:
RS^2 = ST^2 - TR^2 = 13^2 - 5^2 = 169 - 25 = 144
RS = √144 = 12
Therefore, the ratio of the measures of side BC to side RS is 6:12, which can be simplified to 1:2.
So, the correct answer is 1:2.