The answer is: 22.4339811320566038 mi. → Consider rounding to 22.43 mi. _______________________________________________________ (Note: Do not forget the units, in "miles", which can be abbreviated as: "mi."). ____________________________________________________________________ Explanation: _____________________________________________________________________ Let us assume that, at the beginning, Joan is leaving her own house to pick up Kash, first. _____________________________________________________________________ Then, the answer to our problem is the sum of the length of all sides of the triangle given, remember that each "unit" on the graph represents miles. _____________________________________________________________________ We can solve this using the Pythagorean theorem: _____________________________________________________________________ a² + b² = c<span>² ; in which: c = the distance from Joan's house to Kash's house; b = the distance from Kash's house to Gary's house; a = the distance from Gary's house to Joan's house; _____________________________________________________________________ Our answer is the sum of: "a + b + c". _____________________________________________________________________ Using the graph, we can the determine the values for: "a" and "b"; Using the Pythagorean theorem, we can determine the value for "c"; then we can add: "a + b + c" to determine our answer. _____________________________________________________________________ From inspecting the graph: _____________________________________________________________________ </span> b = the distance from Kash's house to Gary's house = 8 mi. [miles] ; a = the distance from Gary's house to Joan's house = 5 mi. [miles] ; __________________________________________________________ Using the Pythagorean theorem, we want to solve for "c": __________________________________________________________ a² + b² = c² ; We substitute our known values for "a" and for "b" : _____________________________________________________ 5² + 8² = c² ; Simplify: _____________________________________________________ 25 + 64 = c² ;
89 = c² ; Take the positive square root of both sides to solve for "c"; _______________________________________________________ √89 = √(c²) ; c = √89 = 9.4339811320566038 _______________________________________________________ Now, we can find our answer: _______________________________________________________________ a + b + c = 5 + 8 + (9.4339811320566038) = 22.4339811320566038 mi. <span>→</span> Consider rounding to 22.43 mi. ; which is our answer.
