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?

2 Answers
Jul 9, 2017

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

Jul 10, 2017

#"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"#