Question

in a small community, mallory road, shel road, and bentley road form a triangle. their lengths are shown as shown.
(the diagram is not drawn to scale.)
based on this information, what is the longest road and the shortest road?
a the longest road is mallory road and the shortest road is bentley road.
b the longest road is shel road and the shortest road is mallory road.
c the longest road is bentley road and the shortest road is shel road.
d the longest road is mallory road and the shortest road is shel road.

Explanation:

Step1: Apply the triangle angle - side relationship

In a triangle, the larger the angle, the longer the side opposite it.
The sum of angles in a triangle is \(180^{\circ}\). Let the angles of the triangle be \(A = 67^{\circ}\), \(B\), and \(C\).
We know that \(A + B + C=180^{\circ}\).

Step2: Compare the angles

Let's assume the sides opposite the angles are \(a\) (opposite \(A = 67^{\circ}\)), \(b\), and \(c\).
The side - angle relationship: If \(A>B>C\), then \(a > b>c\).
The side opposite the largest angle is the longest side, and the side opposite the smallest angle is the shortest side.
The largest angle is \(67^{\circ}\) (opposite Shelly Road), and the smallest angle (by calculation of the third angle: \(180-(67 + 57)=56^{\circ}\)) is opposite Bentley Road.

Answer:

A. The largest road is Shelly Road and the shortest road is Bentley Road.