Given EP = FP and GQ = FQ, what is the perimeter of ΔEFG?

Given:

In the given ΔEFG,

EP = FP and GQ = FQ

Again,

EP =

FP =

FQ =

GQ =

PQ =

To find the perimeter of ΔEFG.

Formula

In this given triangle, EG║PQ and EG = PQ

Now,

By given condition,

----- (1)

---------(2)

From (1) we get,

Putting this value into (2) we get,

or,

From (1) we get,

or,

or,

So,

EF = = unit

FG = unit

PQ = unit

EG = unit

The perimeter of ΔEFG = EF+FG+EG = 16+10+12 unit = 38 unit

Hence,

The perimeter of the given triangle is 38 unit.

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