What is the perimeter of a right triangle where a = 64 millimeters and c = 80 millimeters?

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.