Question

How do you find the dimensions of a rectangle whose perimeter is 52 m and whose area is 160 m?

Answer 1

The dimension of rectangle is `l=16 , b=10`

Explanation:

Perimeter of rectangle is `p=2(l+b) =52`, `l` is length and `b` is breadth.
Area of rectangle is `A=l*b =160 :. l=160/b ; :. 2(160/b+b)=52 or (160/b+b)=26 or (160+b^2)/b=26 or 160+b^2=26b or b^2-26b+160=0 or b^2-16b-10b+160=0 or b(b-16) -10(b-16) =0 or (b-16)(b-10)=0 :. b=16 or b=10`
If `b=16 ; l=160/16=10` and if `b=10 ; l=160/10=16`

The dimension of rectangle is `l=16 , b=10` [Ans]