Answer:
B
Step-by-step explanation:
To find the length of the longest side of the triangle, first sketch the triangle. A graph paper is not needed here.
In this case we have a right-angled triangle, since the ends of the adjacent side has the same y-coordinate of 1 and the opposite side has the same y-coordinate of 5.
In a right-angled triangle, the hypotenuse side is the longest. The length of the hypotenuse side can be found using 2 methods.
1) Pythagoras' Theorem
a² +b²= c²
(adjacent)² +(opposite)²= (hypotenuse)²
Length of adjacent
= 5 -(-2)
= 7 units
Length of opposite side
= 4 -1
= 3 units
(hypotenuse)²
= 7² +3²
= 58
hypotenuse= [tex] \sqrt{58} [/tex]
2) Distance formula
Since we know that the hypotenuse side is the longest, we can simply find the length of the hypotenuse side instead of calculating the length of each side.
[tex]\boxed{{\text{Distance between 2 points}= \sqrt{(y_1 - y_2)^{2} + (x_1 - x_2)^{2} } }}[/tex]
Length of longest side
= distance between (5, 4) and (-2, 1)
[tex] = \sqrt{(4 - 1) {}^{2} + (5 - ( - 2)) {}^{2} } [/tex]
[tex] = \sqrt{3 {}^{2} + {7}^{2} } [/tex]
[tex] = \sqrt{58} [/tex]
Thus, the length of the longest side is [tex] \sqrt{58} [/tex] units.
