The answer is: 22.4339811320566038 mi.
→ Consider rounding to 22.43 mi.
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(Note: Do not forget the units, in "miles", which can be abbreviated as: "mi.").
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Explanation:
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Let us assume that, at the beginning, Joan is leaving her own house to pick up Kash, first.
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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.
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We can solve this using the Pythagorean theorem:
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a² + b² = c² ; 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;
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Our answer is the sum of: "a + b + c".
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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.
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From inspecting the graph:
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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] ;
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Using the Pythagorean theorem, we want to solve for "c":
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a² + b² = c² ; We substitute our known values for "a" and for "b" :
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5² + 8² = c² ; Simplify:
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25 + 64 = c² ;
89 = c² ; Take the positive square root of both sides to solve for "c";
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√89 = √(c²) ; c = √89 = 9.4339811320566038
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Now, we can find our answer:
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a + b + c = 5 + 8 + (9.4339811320566038) = 22.4339811320566038 mi.
→ Consider rounding to 22.43 mi. ;
which is our answer.
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