a rectangular carpet has an area of 96 sq/m and a diagonal of 8m. find the perimeter of the carpet?
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Step-by-step explanation:
Area of rectangular carpet = 120 sq meters. Also area of a rectangle is product of its length(l) and breadth(b). So, area = l * b = 120
So l = 120 / b (by cross multiplying) …..(i)
Perimeter of rectangle is = 46 meter. Also the perimeter of a rectangle can be written as Perimeter= 2 * (l + b)
So 46 = 2 * (l + b) …..(ii)
Substituting (i) in (ii) we get,
46 = 2 * ( 120/b + b)
which can also be written as,
b^2 - 23b + 120 = 0
By middle spilting we get
b^2 - 15b - 8b + 120 = 0
so b = 15 or 8.
Assume b=8 then from (i) l = 120/8 => l=15
Now in a right angled triangle
H^2 = L^2 + B^2
H^2 = (15)^2 + (8)^2
H^2 = 225 + 64 = 289
therefore H = 17
So the length of the diagonal is 17 meters.
hope it helps...!!!
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