Question

there is a slide in a park; one of its side walls has been painted in some colour with message "KEEP THE PARK GREEN AND CLEAN". If the sides of walls are in 12:17:25 and parimeter is 540m. find the area painted in colour.which value is depicted by the message?

Answer 1

let all sides-x
peremeter-540
12x+17x+25x=540
54x=540
x=540÷54

Answer 2

let the sides be 1,2&3.
multiply the sides of the wall by x, we get,
12x, 17x & 25x.
therefore, 12x+17x+25x=540m
=> 54x=540m
=> x=540/54=10
=> 1 = 12x=12×10=120m
=> 2 = 17x=17×10=170m
=> 3 = 25x=25×10=250m

finding the area of the wall by heron's formula,
where s=(1+2+3)/2=(120+170+250)/2
= 540/2= 270

heron's formula=> √s(s-1)(s-2)(s-3)
=> √270(270-120)(270-170)(270-250)
=> √270(150)(100)(20)
=> 10√3×90×3×50×4×5
=> 10×3×2√90×50×5
=> 60√22500
=> 60×150=9000m^2
therefore, area of the wall is 9000m^2
value depicted is cleanliness, we must keep our environment clean.
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