Find the dimensions of a rectangle whose perimeter is 28 meters and whose area is 40 square meters.
Let the length and the breath of the rectangle be l and b respectively.
According to the given condition
l × b = 40 m2 ( area = length × breath)…………..1
and
Perimeter = 2(l + b)
2(l + b) = 28
⇒ l + b = 14
⇒ b = 14 –l
Putting value of b in 1
l( 14 - l) = 40
⇒ l2 – 14 l + 40 = 0
⇒ l2 – 10l – 4l + 40 = 0
⇒ l( l - 10) – 4(l - 10) = 0
⇒ (l - 4) ( l - 10) = 0
⇒ l = 4 or 10 m
Hence length is 4 m
And breath is 10 m.