The perimeter of a rectangular field is 82 m and its area is `400 m^(2).` Find the dimensions of the field.

Explanation

We know that 2(length + breadth) = perimeter.
`:." "("length + breadth")=(1)/(2)xx" premeter "=(1)/(2)xx82m=41m.`
Let the length of the field be x metres.
Then, its breadth `=(41-x)m`.
`:." ""area of the field "=x(41-x)m^(2)=(41x-x^(2))m^(2).`
But, area `=400m^(2)(" given")`
`:." "41x-x^(2)=400`
`implies" "x^(2)-41x+400=0impliesx^(2)-25x-16x+400=0`
`implies" "x(x-25)-16(x-25)=0implies(x-25)(x-16)=0`
`implies" "x-25=0" or "x-16=0impliesx-25" or "x=16.`
`:." "length of the field = 25 m and breadth of the field = 16 m.