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Sahil

· started a discussion

· 1 Months ago

Kindly brief the formula used with proof for understanding (Question: 108123.0 )

Sir yeh kon sa formula hai :
Area of equilateral trianble = 1/2 * (a+b+c) * side of triangle

Question:
From any point inside an equilateral triangle, the lengths of perpendiculars on the sides are ‘a’ cm, ‘b’ cm and ‘c’ cms. Its area (in cm2) is:
Options:
A) \(\cfrac{\sqrt[]{2}}{3}\) (a + b + c)2
B) \(\cfrac{\sqrt[]{2}}{3}\) (a + b + c)
C) \(\cfrac{\sqrt[]{3}}{3}\) (a + b + c)2
D) \(\cfrac{\sqrt[]{3}}{3}\) (a + b + c)
Solution:
Ans: (c)

Let the side of the equilateral triangle be x cm.

Area of the equilateral triangle 


ravi

· commented

· 1 Months ago

jo thee triangles banege unke area ka addition hai

Sahil

· commented

· 1 Months ago

@Knowledge Expert How there will be 3 triangles ? can you please share a diagram and 3 triangles after perpendiculars are dropped, for better understanding....

Knowledge Expert

· commented

· 1 Months ago

Dear Student
let centre be the point from where perpendiculars are dropped on the respective sides of the equilateral triangle of side a.
there will be 3 triangles
so, area
1/2a(x+y+z)=1/2ax+1/2ay+1/2az
by equating it with actual formulae for area.
we will get the value of x
and substituting it, we can get the area.
regards
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