Question

If the difference between the length and breadth of a rectangle is 20 m and its area is 1056 m², then calculate the perimeter of the rectangle.​

Answer 1

Answer:

l-b=20 & lb=1056

(l+b)^2-(l-b)^2=4lb

by substituting the given values

l+b=68..perimeter =2(l+b)=136

Answer 2

Answer:

Perimeter of the rectangle = 136m and length of the rectangle =44m, breadth of the rectangle= 24m

Step-by-step explanation:

Given: difference between the length and breadth of rectangle is 20m.

       area of rectangle = 1056m².

To find :perimeter of rectangle.

solution:

let l and b be the length and breadth of the rectangle.

since difference between l and b is 20,

⇒l-b = 20m then l = b+20--------eq(1)

also since area of rectangle =  1056m²        

                 l × b = 1056

       (  b + 20 )× b = 1056   (from eq (1))

         b² + 20b =1056

       b² + 20b -1056 = 0 be a quadratic equation

b²+44b-24b-1056 = 0

b(b+44)-24(b+44) = 0 ⇒ (b+44)(b-24)=0

      b +44 =0 and b-24 =0

∴b = 24 and b = -44(negative, not possible)

since breadth cannot be a negative value, so b=24m

then from eq (1)  l= b+20 = 24+20 =44m

∴perimeter of a rectangle = 2×( l+ b) = 2×(44+24) = 2×68= 136m.

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