SOLUTION: The vertices R, S, T of the right triangle RST are the centers of 3 circles. The circles with centers R and T are externally tangent to the circle with center S. Find the perimeter
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Question 474463: The vertices R, S, T of the right triangle RST are the centers of 3 circles. The circles with centers R and T are externally tangent to the circle with center S. Find the perimeter, in cm, of triangle RST.
Circle with center Diameter
R 6
S 18
T 14
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
The diameter of R is equal to 6 so the radius of R is equal to 3.
The diameter of S is equal to 18 so the radius of S is equal to 9.
The diameter of T is equal to 14 so the radius of T is equal to 7.
The picture below shows what is happening.
Radius of circle R is 3.
Radius of circle S is 9.
Radius of circle T is 7.
RS is equal to 12 which is the radius of circle R plus the radius of circle S.
ST is equal to 16 which is the radius of circle S plus the radius of circle T.
RT is the hypotenuse of triangle RST which can be found using the formula:
RT squared = RS squared plus ST squared.
This makes RT squared equal to 12 squared plus 16 squared which is equal to 400.
this makes RT equal to the square root of 400 which is equal to 20.
The dimensions of triangle RST are:
RS = 12
ST = 16
RT = 20
The perimeter of triangle RST is therefore equal to 48.
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