In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 64 millimeters and c = 80 millimeters, what is the perimeter? If necessary, round to the nearest tenth.
millimeters
What is the perimeter of a right triangle where a = 64 millimeters and c = 80 millimeters?
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To find the perimeter of the right triangle, we need to calculate the length of the second leg ( b ) using the Pythagorean theorem, which states:
[
c^2 = a^2 + b^2
]
Given:
– ( a = 64 ) mm
– ( c = 80 ) mm
First, we can substitute ( a ) and ( c ) into the Pythagorean theorem:
[
80^2 = 64^2 + b^2
]
Calculating the squares:
[
6400 = 4096 + b^2
]
Now, isolate ( b^2 ):
[
b^2 = 6400 – 4096 = 2304
]
Next, take the square root to find ( b ):
[
b = sqrt{2304} = 48 text{ mm}
]
Now that we have both legs ( a ) and ( b ), we can calculate the perimeter ( P ):
[
P = a + b + c = 64 + 48 + 80
]
[
P = 192 text{ mm}
]
Therefore, the perimeter of the triangle is 192 millimeters.