A circle with radius r is inscribed into a right triangle. Find the perimeter of the triangle if: The point of tangency divides
the hypotenuse into 5 cm and 12 cm segments.
1 answer:
Answer:
40 cm
Step-by-step explanation:
If we let r represent the radius of the circle, the legs of the triangle have length 5+r and 12+r. Then the Pythagorean Theorem tells us ...
(5 +12)^2 = (5 +r)^2 +(12 +r)^2
5^2 +2·5·12 +12^2 = 5^2 +2·5·r +r^2 + 12^2 +2·12·r +r^2
120 = 34r +2r^2 . . . . subtract 5^2 +12^2
60 +8.5^2 = 8.5^2 +17r +r^2 . . . . . . divide by 2, add (17/2)^2
11.5 = 8.5 +r . . . . . . . . . . . . . . . . . . . take the square root (negative root is extraneous)
3 = r
The radius of the circle is 3 cm. The perimeter of the triangle is the sum of the side lengths:
(5 +3) cm + (12 +3) cm + (5+12) cm = 2(5 +12 +3) cm = 40 cm
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Answer:
10.44
Step-by-step explanation:
First plot each of the points on to a graph at their respective positions.
Following that create a 90° triangle out of the points. This will create a 3 by 10 triangle. (3 to 0 is 3) (-8 to 2 is a difference of 10)
You can then use the pythagorean theorem .
Insert the lengths of each of the sides that we got earlier which would be 3 and 10 into the equation.
Since we want to find the hypotenuse which is equal to c we work the equation to 9+100 = which in turn is 109 =
Then take the square root of 109 to remove the square from the c to get c = 10.44
Answer:
C
Step-by-step explanation:
42%= = 0.42