Question

A room 5m long and 4m wide is surrounded by a verandah. If the verandah occupies an area of 23m^2, find the width of the verandah.

Answer 1

surface area of verandha
l=5
b=4
h=x
surface area of verandha = 2 (lb+bh+hl)
23=2 (5×4+4+x+x×5)
23=2 (20+4x+5x )
23=40+8x+10x
23=40+18x
23-40=18x
17=18x
17/18=x

Answer 2

Answer:

Width of the veranda is 1.04 meter.

Step-by-step explanation:

We are given that,

Dimensions of the room are 5 meter × 4 meter.

So, area of the room = Length × Width = 5×4 = 20 m²

Let the width of the veranda = x meter.

As, the veranda is on all the sides of the room.

The dimensions of the veranda are (5+2x) and (4+2x) meters respectively.

So, the area of the region outside the room = $(5+2x)(4+2x)$

Since, the area of the veranda = 23 m²

We have,

Area outside the room - Area of the room = 23 m²

i.e. $(5+2x)(4+2x)-20=23$

i.e. $20+10x+8x+4x^2-20=23$

i.e. $4x^2+18x-23=0$

i.e. x= -5.54 m and x= 1.04 m

Since, the width of the veranda cannot be negative.

So, we have that,

Width of the veranda is 1.04 meter.