Which answer is correct ? Please explain why !!
2 answers:
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Answer:
26.1miles
Step-by-step explanation:
If three cities A, B and C form a right triangle on a map, and the Cities B and C are the furthest apart, then the distance between cities B and C will be the hypotenuse of the triangle.
If cities A and B are 14 miles apart, then |AB| = 14miles
Also if cities A and C are 22 miles apart, then |AC| = 22miles.
To get |BC| which is the distance between cities B and C, we will use the Pythagoras theorem.
|BC|² = |AB|² + |AC|²
|BC|² = 14²+22²
|BC|² = 196+484
|BC|² = 680
|BC| = √680
|BC| = 26.1miles
This means that cities B and C are 26.1miles apart
The ΔABR ≅ ΔACR are congruent by SAS theorem
Option D is the correct answer.
The missing diagram is attched with the answer.
<h3>What is a Triangle ?</h3>A triangle is a polygon with three sides , three vertices and three angles.
SAS will be used to prove the congruence of ΔABR ≅ ΔACR
In both the triangle we have a common side , AR
AB = AC (given)
∠ B A R = ∠R A C ( given equal)
So as the two side and the included angle is equal
Therefore the ΔABR ≅ ΔACR are congruent by SAS theorem
Option D is the correct answer.
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