Question

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

Answer 1

Given:

In the given ΔEFG,

EP = FP and GQ = FQ

Again,

EP = $4y+2$

FP = $2x$

FQ = $3x-1$

GQ = $4y+4$

PQ = $x+2y$

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 = $\frac{1}{2}$PQ

Now,

By given condition,

$2x = 4y+2$ ----- (1)

$3x-1 =4y+4$---------(2)

From (1) we get, $4y = 2x-2$

Putting this value into (2) we get,

$3x-1 = 2x-2+4$

or, $x = 3$

From (1) we get,

$4y = 2(3)-2$

or, $4y = 4$

or, $y = 1$

So,

EF = $2x+4y+2$ = $2(3)+4(1)+2 = 12$ unit

FG = $3x-1+4y+4 = 3(3)-1+4(1)+4 = 16$ unit

PQ =$3+2(1) = 5$ unit

EG = $2(5) = 10$ unit

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

Hence,

The perimeter of the given triangle is 38 unit.