Question

What is the length of the longest side of a triangle that has the vertices (-2, 1), (5, 1), and (5, 4)?

Answer 1

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= $\sqrt{58}$

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.

$\boxed{{\text{Distance between 2 points}= \sqrt{(y_1 - y_2)^{2} + (x_1 - x_2)^{2} } }}$

Length of longest side

= distance between (5, 4) and (-2, 1)

$= \sqrt{(4 - 1) {}^{2} + (5 - ( - 2)) {}^{2} }$

$= \sqrt{3 {}^{2} + {7}^{2} }$

$= \sqrt{58}$

Thus, the length of the longest side is $\sqrt{58}$ units.