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?

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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?

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Answer 1 · 2017-07-09T14:42:24

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 · 2017-07-10T08:10:02

$"width " =1m$

Explanation:

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

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

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

$"distribute and equate to zero"$

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

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

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

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

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

$x>0rArrx=1$

$color(blue)"As a check"$

$5+2x=5+2=7$

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

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

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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

Explanation:

Explanation:

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