Answer: The length of AC is: " 2√2 units " . ____________________________________________________ Explanation: ____________________________________________________ Note: (not to scale): ____________________________________________________ C | \ | \ 2 | \ "c" |-- \ | \ |_|______\ A •2 (point –at which right angle forms) _______________________________________________________ Use the "Pythagorean theorem" (since this is a right triangle) to solve for the length of AC— which is represented by "c" :
a² + b² = c² ;
↔ c² = a² + b² ; Solve for "c" ;
Given: "a = 2 ; b = 2 " ;
→ c² = 2² + 2²
→ c² = 4 + 4 ;
→ c² = 8 ;
Take the "positive square root" of each side of the equation; to isolate "c" on one side of the equation; & to solve for "c" ;
→ √(c²) = √8 ;
→ c = √8 ;
→ √8 = √4 * √2 = 2√2 . _____________________________________________________ Answer: The length of AC is: " 2√2 units " . _____________________________________________________
