Question

As shown in the figure, Avinash is standing near his house. He can choose from two roads to go to school. Which way is shorter? Explain why.

Answer 1

Hey there !

Solution :

Inequalities of Triangle :

According to the inequalities of triangle, the sum of two sides is always greater than the third longest side. That is,

In a Right Angled Triangle, the sum of the opposite and adjacent side is always greater than the Hypotenuse which is the longest side of the triangle.

Another way to find the longer side of a triangle is by angle measurement method.

The side opposite to the greatest angle is always the greatest side of a triangle. This also can be explained by inequalities of a triangle.

So coming to the question asked,

Well, The triangle given in the figure appears to be a right angled triangle. Hence the sides can be labelled as :

AB = Adjacent side ; BC = Opposite side ; AC = Hypotenuse 

So let the reference angle be ∠ C.

So  According to inequalities, AC must be shorter path. 

This is because, 

AC is the longest side as it is the hypotenuse. Hence the sum of other two sides will be greater than this side. Hence AC is the shortest path that must be travelled by Avinash.

Hope my answer helped !