Question

A square hut with side lengths of 5 m is to be surrounded by a veranda of width x metres. Find the width of the veranda if its area is to be 24 m^2?

Answer 1

WIdth of veranda`=1m`

Explanation:

Total area of hut + veranda
`=25+24=49m^2`

So veranda sides`=7m`

`7m-5m=2m`

So veranda width`=1m`

~~~~~~~~~~~~~~~~~~~~~~~

`Check:`

Veranda on 2 sides`=1m` by `7m=7m^2*2=14m^2`

Veranda on 2 sides`=1m` by `5m=5m^2*2=10m^2`

`14m^2+10m^2=24m^2=`area of veranda

Answer 2

`"width " =1m`

Explanation:

`"the length of the hut and veranda " =5+2x`

`rArr" the width of the hut and veranda " =5+2x`

`rArr(5+2x)^2-25=24`

`"distribute and equate to zero"`

`rArr25+20x+4x^2-25-24=0`

`rArr4x^2+20x-24=0larr" common factor of 4"`

`rArr4(x^2+5x-6)=0`

`rArr(x+6)(x-1)=0`

`rArrx=-6" or " x=1`

`x>0rArrx=1`

`color(blue)"As a check"`

`5+2x=5+2=7`

`"area of veranda "=7^2-5^2=49-25=24larr" True"`

`rArr"width of veranda " =1" m"`