Calculate the perimeter of a rectangle whose area is 25x2 – 35x + 12.
Answers
• Area of Rectangle = 25x² – 35x + 12
\green{\large{ \underline{\mathcal{\star \: To \: Find : }}}}
⋆ToFind:
• Perimeter of the Rectangle.
\green{\large{ \underline{\mathcal{\star \: Solution : }}}}
⋆Solution:
\blacksquare \: \scriptsize\boxed {\bold{Area \: of \: Rectangle = Length \times Breadth}}■
AreaofRectangle=Length×Breadth
So, By Factoring 25x² – 35x + 12, the Length and Breadth can be obtained.
\large \leadsto \tt{25 {x}^{2} - 35x + 12 = 0}⇝25x
2
−35x+12=0
\large \leadsto \tt{25 {x}^{2} - 15x - 20x + 12 = 0}⇝25x
2
−15x−20x+12=0
\large \leadsto \tt{5x(5x - 3) - 4(5x - 3) = 0}⇝5x(5x−3)−4(5x−3)=0
\pink{\large \leadsto \tt{(5x - 3)(5x - 4) = 0}}⇝(5x−3)(5x−4)=0
So, the Length and Breadth are (5x – 3)(5x – 4).
\blacksquare \: \scriptsize\boxed {\bold{Perimeter = 2(Length + Breadth)}}■
Perimeter=2(Length+Breadth)
\large \leadsto \tt{Perimeter= 2(5x - 3 + 5x - 4)}⇝Perimeter=2(5x−3+5x−4)
\orange{\large \leadsto \boxed{\tt{Perimeter= 2(10x - 7)}}}⇝
Perimeter=2(10x−7)
\huge{\red{\ddot{\smile}}}
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Hello friend
Hope this helps you
Area of rectangle = 25x^2 - 35x + 12
=25x^2 - 15x - 20x + 12
= 5x(5x - 3) - 4(5x - 3)
=(5x - 3)(5x - 4)
=x=3/5 or 4/5
therefore, l=4/5 and b=3/5
Perimeter = 2(l + b)
=2(3/5 + 4/5)
=2(7/5)
=14/5
=2.8
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