Answer: The perimeter of the triangle given is: " 24 units " . ______________________________________________________ Explanation: ______________________________________________________ To find the perimeter of the triangle, we add up the lengths of all 3 (THREE) sides of the triangle; and we have the answer! ______________________________________________________ The triangle given is a "right triangle.
We are given the length of 2 (TWO) of the sides: "6 units" ; and "10 units (the length of the hypotenuse). ___________________________________________________________ We can find the "unknown side length" by using the "Pythagorean theorem" (since this is a "right trangle"):
→ a² + b² = c² ;
in which : "c" is the hypotenuse; which is: "10" (given);
Let "b" represent the known side length, which is "6" (given).
Solve for "a" (the "unknown" side length).
→ a² + 6² = 10² ; Solve for "a" ;
→ a² = 10² – 6² = 100 – 36 = 64 .
↔ a² = 64 .
Now, take the positive square root of each side of the equation; to isolate "a" on one side of the equation; & to solve for "a" ;
→ ⁺√(a²) = √64 ;
→ a = 8 . __________________________________________________ Now, to find the "perimeter" of the triangle, we add up all of the side lengths:
6 + 8 + 10 = 14 + 10 = 24 . __________________________________________________ Answer: The perimeter of the triangle given is: " 24 units " . __________________________________________________