Question
Download Solution PDFThe length of a rectangular fenced area is 15 m more than its breadth. Its area is 31096 m2 . Its breadth (in m) is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Area = 31096 m2
Length (l) = Breadth (b) + 15
Calculations:
Set up the equation using the area formula.
Formula: Area = Length × Breadth
⇒ 31096 = (b + 15) × b
⇒ 31096 = b2 + 15b
⇒ b2 + 15b - 31096 = 0
Solve the quadratic equation for 'b'.
We can solve this by finding two numbers whose product is -31096 and whose difference is 15. The numbers are 184 and -169.
⇒ (b + 184)(b - 169) = 0
This gives two possible values for b: b = -184 or b = 169.
Since the breadth cannot be negative, we take the positive value.
∴ The breadth of the rectangular fenced area is 169 m.
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