The perimeter of a rectangle is 82m and its area is 400m2 the breadth of rectangle is?
Answers
Correct question:-
Is it possible to design a rectangular park of perimeter 80 and area 400m²? If so find its length and breadth.
Answer:-
Let the length and breadth of the park be L and B.
Perimeter of the rectangular park = 2 (L + B) = 80
So,
L + B = 40
B = 40 – L
Area of the rectangular park = L × B = L(40 – L) = 40L – L² = 400
L² – 40 L + 400 = 0
Hence, it is a quadratic equation.
Comparing the equation with ax² + bx + c = 0, we get
a = 1, b = -40, c = 400
Since, Discriminant = b2 – 4ac
→ (-40)2 – 4 × 400
→ 1600 – 1600 = 0
Thus, b² – 4ac = 0
Therefore, this equation has equal real roots. Hence, the situation is possible.
Root of the equation:-
L = –b/2a
L = (40)/2(1) = 40/2 = 20
Therefore, length of rectangular park, L = 20 m
Therefore, the length, L = 20 m and breadth, B = 40 – L = 40 – 20 = 20 m.