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The Area of a Small Rectangular Plot is 84 M2. If the Difference Between Its Length and the Breadth is 5 M; Find Its Perimeter. - Mathematics

Sum

The area of a small rectangular plot is 84 m2. If the difference between its length and the breadth is 5 m; find its perimeter.

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Solution

Area of a rectangular plot = 84 m2
Let breadth = x m
Then length = (x + 5) m
Area = l x b
x(x + 5) = 84
x2 + 5x – 84 = 0
=> x2+ 12x – 7x – 84 = 0
=> x(x + 12) – 7(x + 12) = 0
=> (x + 12) (x – 7) = 0
Either x + 12 = 0, then x = -12 which is not possible being negative
or x – 7 = 0, then x = 7
Length = x + 5 = 7 + 5 = 12m
and breadth = x = 7 m
Perimeter = 2(l + b) = 2(12+ 7) = 2 x 19 m = 38 m

Concept: Perimeter of a Rectangle
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APPEARS IN

Selina Concise Mathematics Class 8 ICSE
Chapter 20 Area of a Trapezium and a Polygon
Exercise 20 (B) | Q 4 | Page 227
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