Mathematics
The perimeter of a rectangular field is 28 m and its area is 40 sq. m. Its sides are :
8 m and 6 m
4 m and 10 m
10 m and 6 m
3 m and 11 m
Quadratic Equations
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Answer
Let length and breadth of rectangular field be l and b meters respectively.
By formula,
⇒ Perimeter = 2(l + b)
⇒ 28 = 2(l + b)
⇒ l + b = 14
⇒ l = 14 - b ……(1)
By formula,
⇒ Area = lb
⇒ 40 = lb
Substituting value of l from equation (1), we get :
⇒ 40 = b(14 - b)
⇒ 40 = 14b - b2
⇒ b2 - 14b + 40 = 0
⇒ b2 - 10b - 4b + 40 = 0
⇒ b(b - 10) - 4(b - 10) = 0
⇒ (b - 4)(b - 10) = 0
⇒ b - 4 = 0 or b - 10 = 0
⇒ b = 4 or b = 10.
If b = 4,
l = 14 - b = 14 - 4 = 10.
If b = 10,
l = 14 - b = 14 - 10 = 4.
∴ Sides = 4 m and 10 m.
Hence, Option 2 is the correct option.
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