area of a rectangle is (3a^2+5ab+2b^2) one of its side is (a+b) what is the perimeter​

2 thoughts on “area of a rectangle is (3a^2+5ab+2b^2) one of its side is (a+b) what is the perimeter​”

1. Concept used-:

   ~Here the concept of Area & perimetre is used. By using the area formula of rectangle we will find the length. Then after súbsitúte the value of length and breath in the Perimeter formula.

   Formula used

   [tex] \to \bold\pink {Area\:of \:rectangle= length×breath}[/tex]

   [tex]\to\bold \purple{Perimeter\:of \: rectangle=2×(length×breath)}[/tex]

   Solution

   • Area of rectangle = 3a²+5ab+2b² sq.unit
   • side (breath) = a+b unit

   Let us assume the length as L

   Area of rectangle= length× breath

   [tex]\sf{\implies3a²+5ab+2b² =L× (a+b)}\\ \\ \sf{ \implies L= \frac{3a²+5ab+2b²}{a+b}} \\ \\ \sf{ \implies \red{L = 3a+2b\:units }}[/tex]

   therefore the length of the rectangle is 3a+2b units

   Now let us find the perimeter.

   perimeter of rectangle=2×( length+breath)

   [tex]\sf{ \implies perimeter \: of \: rectangle= 2×(3a+2b +(a+b))}[/tex]

   [tex]\sf{ \implies perimeter \: of \: rectangle= 2× (4a+3b)} \\ \\ \sf{ \implies \green{perimeter \: of \: rectangle = 8a +6b\:units}}[/tex]

   Therefore the perimetre of the rectangle is 8a +6b units

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2. Given:-

   • Area of rectangle is 3a² + 5ab + 2b².

   • One of its side is a + b .

   To Find:-

   • Another side of rectangle.

   • Perimeter of rectangle.

   Solution:-

   Here, Area of rectangle = Length × Breadth

   Let the another side be [tex]x[/tex] units.

   Now, [tex]a + b \times x = 3a^{2} + 5ab + 3b^{2}[/tex]

   ⇒ [tex]x = \dfrac{3a^{2} + 5ab + 2b^{2}}{a + b}[/tex]

   ⇒ [tex]x = 3a + 2b[/tex]

   So, Another side of rectangle will be 3a + 2b units.

   Since, Perimeter of rectangle = [tex]2 ( L + B )[/tex]

   ⇒ [tex]2 [(a + b) + (3a + 2b)][/tex]

   ⇒ [tex]2 \times ( 4a + 3b )[/tex]

   ⇒ [tex]8a + 6b[/tex]

   Hence, Perimeter of the rectangle is 8a + 6b units .

   Some Important terms:-

   • Area of square = [tex](Side)^{2}[/tex]

   • Perimeter of square = 4 × Side

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