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17 votes
17 votes
What is the value of q

What is the value of q-example-1
User Prash
by
2.9k points

1 Answer

11 votes
11 votes

Answer:

Triangles QST and RST are similar. Therefore, the following is true:

q s

--- = ---- This results in 10q=rs.

r 10

Also, since RST is a right triangle, 4^2 + s^2 = q^2.

Since QST is also a right triangle, s^2 + 10^2 = r^2.

4 s

Also: ---- = ----- which leads to s^2 = 40

s 10

Because of this, 4^2 + s^2 = q^2 becomes 16 + 40 = 56 = q^2

Then q = sqrt(56) = sqrt(4)*sqrt(14) = 2*sqrt(14) (answer)

User Golkarm
by
2.2k points
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