Q: The sketch below shows a plan of a living room. The length of the room is (2x-1) and the width of the room is (x+1) where x is measured in meters

Given that the area of the room must be at least 135 square meters and the total length of the walls cannot exceed 54 meters.

(a) Find the set of values of x that satisfy both constraints.

(b) Hence find the maximum and minimum values of the area and perimeter of the room.

My attempt:

for part a

$\displaystyle p = (2x-1)+(2x-1)+(x+1)+(x+1)$

$\displaystyle p=6x$

but p<54

$\displaystyle 6x<54$

x<9

therefore x+1<9+1 = x+1<10

and $\displaystyle 2(x)<18 $

$\displaystyle 2x-1<17 $

thus x+1<10 ; 2x-1<17

please point out if i did anything wrong

for part b

i dont know how to answer part b

please help

thank you