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The perimeter of rectangle is 24 cm and area of rectangle is 35cm^2. What are the dimensions of the rectangle?(a) l=9, b=5(b) l=12, b=5(c) l=5, b=7(d) l=5, b=5I had been asked this question in exam.I need to ask this question from Solution of Quadratic Equation by Squaring Method in portion Quadratic Equation of Mathematics – Class 10

Answer»

Right answer is (C) L=5, b=7

Best explanation: Let the length of the rectangle be l cm and breadth be b cm.

Perimeter of rectangle = 24

2(l+b)=24

l+b=12

l=12-b(1)

Now, the area of rectangle is 35 cm^2

l×b=35(2)

SUBSTITUTING (1) in (2)

(12-b)b=35

12b-b^2=35

b^2-12b+35=0

b^2-12b=-35

Adding \(\frac {b^2}{4}\) on both sides, where b=-12

b^2 – 12b + \(\frac {-12^2}{4}=\frac {-12^2}{4}\) – 35

b^2 – 12b + \(\frac {144}{4}=\frac {144}{4}\) – 35

b^2 – 12b + \(\frac {144}{4}=\frac {4}{4}\)

\((b-\frac {12}{2})\)^2=\((\frac {2}{2})\)^2

b-\(\frac {12}{2}\)=±\(\frac {2}{2}\)

b = \(\frac {2}{2}+\frac {12}{2}=\frac {14}{2}\) = 7 and b = \(\frac {-2}{2}+\frac {12}{2}=\frac {10}{2}\) = 5

The length of the rectangle is l=12-b=12-7=5 and l=12-5=7

The length and breadth of the rectangle are 7 and 5 or 5 and 7.


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