Question

HELPPP!!!!

ANSWER ONLY IF YOU KNOW IF THE QUESTION IS CORRECT I'LL GIVE 30 EXTRA POINT (50 point total) EXPLAIN HOW

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

Answer 1

38 units

Explanation:

EP = FP , then

4y + 2 = 2x → (1)

GQ = FQ , then

4y + 4 = 3x - 1 ( subtract 4 from both sides )

4y = 3x - 5 → (2)

substitute 4y = 3x - 5 into (1)

3x - 5 + 2 = 2x ( subtract 2x from both sides )

x - 3 = 0 ( add 3 to both sides )

x = 3

substitute x = 3 into (1)

4y + 2 = 2(3) = 6 ( subtract 2 from both sides )

4y = 4 ( divide both sides by 4 )

y = 1

Then

EP = 4y + 2 = 4(1) + 2 = 4 + 2 = 6 = FP

GQ = 4y + 4 = 4(1) + 4 = 4 + 4 = 8 = FQ

PQ is a midsegment and is half the length of EG

PQ = x + 2y = 3 + 2(1) = 3 + 2 = 5 , so

EG = 2 × 5 = 10

Then summing the parts for perimeter (P)

P = 6 + 6 + 8 + 8 + 10 = 38