Question

PLEASE HELP IT IS VERY URGENT!!

Answer 1

Step-by-step explanation:

(c)

$In\: \triangle PLM \: \&\: \triangle PLM\\\angle PLM \cong\triangle PFG.. (corresponding \:\angle s) \\\angle LPM \cong \angle FPG.. (common \: \angle s) \\\therefore \triangle PLM\sim\triangle PFG.. (by\: AA\:Postulate) \\PF = PL + LF = 2 + 3 = 5$

By area of similar triangle theorem:

$\frac {A(\triangle PLM)}{A(\triangle PFG)}= \frac{PL^2}{PF^2}\\\therefore \frac {A(\triangle PLM)}{A(\triangle PFG)}= \frac{2^2}{5^2}\\\therefore \frac {A(\triangle PLM)}{A(\triangle PFG)}= \frac{4}{25}\\A(\triangle PLM)\: :\: A(\triangle PFG) = 4 \: :\: 25$