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:
Step-by-step explanation:
The base of the pyramid we need to study is a hexagon.
Let's look at the attached image of an hexagon to understand how we are going to find the area of this figure.
Notice that an hexagon is the combination of 6 exactly equal equilateral triangles in our case of size "2x" (notice that the "radius" of the hexagon is given as "2x")
Therefore the area of the hexagon is going to be 6 times the area of one of those equilateral triangles.
We know the area of a triangle is the product of its base times its height, divided by 2:
We notice that the triangle's height is exactly what is called the "apothem" of the hexagon (depicted in green in our figure) which measures , so replacing this value in the formula above for the area of one of the triangles:
Then we multiply this area times 6 to get the total area of the hexagon (6 of these triangles):
Area of hexagon =
which is the last option given in the list.
Answer:
5
Step-by-step explanation:
15 × = 5