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mel-nik [20]
3 years ago
11

In the diagram below, RA is parallel to ET, and RT is 21 units long. Find the length of ST

Mathematics
1 answer:
pav-90 [236]3 years ago
5 0

Answer:

ST = 12 units

Step-by-step explanation:

As RA is parallel to ET, the angle in R is equal to the angle in T, and the angle in A is equal to the angle in E, so the triangle RAS is similar to the triangle SET.

If RT is 21 units, we have that RS + ST = 21 -> RS = 21 - ST

Using a rule of three with the sides of the triangle (as they are proportional), we have:

RS / ST = AR / ET

(21 - ST) / ST = 6 / 8

4 * (21 - ST) = 3*ST

84 - 4*ST = 3*ST

7*ST = 84

ST = 12 units

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