Given:
In the given ΔEFG,
EP = FP and GQ = FQ
Again,
EP = [tex]4y+2[/tex]
FP = [tex]2x[/tex]
FQ = [tex]3x-1[/tex]
GQ = [tex]4y+4[/tex]
PQ = [tex]x+2y[/tex]
To find the perimeter of ΔEFG.
Formula
- The perimeter of a triangle is the sum of all the sides.
- By Midpoint Theorem we get, a line segment joining the mid points of two sides of a triangle is parallel and half to the third side.
In this given triangle, EG║PQ and EG = [tex]\frac{1}{2}[/tex]PQ
Now,
By given condition,
[tex]2x = 4y+2[/tex] ----- (1)
[tex]3x-1 =4y+4[/tex]---------(2)
From (1) we get, [tex]4y = 2x-2[/tex]
Putting this value into (2) we get,
[tex]3x-1 = 2x-2+4[/tex]
or, [tex]x = 3[/tex]
From (1) we get,
[tex]4y = 2(3)-2[/tex]
or, [tex]4y = 4[/tex]
or, [tex]y = 1[/tex]
So,
EF = [tex]2x+4y+2[/tex] = [tex]2(3)+4(1)+2 = 12[/tex] unit
FG = [tex]3x-1+4y+4 = 3(3)-1+4(1)+4 = 16[/tex] unit
PQ =[tex]3+2(1) = 5[/tex] unit
EG = [tex]2(5) = 10[/tex] unit
The perimeter of ΔEFG = EF+FG+EG = 16+10+12 unit = 38 unit
Hence,
The perimeter of the given triangle is 38 unit.
