Perimeter of a triangle

[Videoorchard]

Hi,

The question below pertains to Guide 3 (Geometry), Chapter 5, Problem Set, Question:13

Doubt:
In the quantity A, they asked us to find the perimeter of the triangle. which is length of all the 3 sides of the triangle. But, the author has taken into count just the sides that is AB & AC, dropping off BC. Similarly perimeter of the "shaded region should be BDC+BC .Again, the author has considered only BDC, What's going on?


P.S: I am aware there is a overlap here (BC) .

[n00bpron00bpron00b]

I am aware there is a overlap here (BC)

This answers your doubt :)

In triangle ABC -
AB & AC are the radius - equal length and AB+AC is the sum of two smaller sides

So perimeter of triangle ABC is AB+AC+BC

Length of Arc - BDC
(x/360) * (2*pi*r)
(120/360) * (2*pi*r)
=> (2*pi*r)/3

Perimeter of the shaded region
Length of arc BDC + BC

Quantity A:
AB+AC+BC
Quantity B:
BDC + BC

BC overlapping - we can subtract it from both sides

Quantity A:
AB + AC - sum of two short legs

Quantity B:
(2*pi*r)/3 - length of curve - travels greater distance

Quantity B greater

[tommywallach]

Thanks, Noob. And Video, you were right there!

-t

[Videoorchard]

Thank you for clearing my doubts guys!

[tommywallach]

(P.S. Sorry if it always seems like I'm getting the last word. This is the easiest way for me to work out which posts I've responded to...by always being the last person to post!)

-t