Question

A rectangular tennis court has a length of (5a + 2b) metres, and a width of (4a – b) metres. Answer the following questions by showing all the working. a) Find the perimeter of the tennis court with respect to a and b.

Answer 1

$\underline{\underline{\sf{\maltese\:\:Question}}}$

• A rectangular tennis court has a length of (5a + 2b) meters, and a width of (4a - b) meters. Find the perimeter of the tennis court with respect to a and b.

$\underline{\underline{\sf{\maltese\:\:Given}}}$

• Length of Rectangular Tennis court = (5a + 2b) meters

• Breadth of Rectangular Tennis court = (4a + b) meters

$\underline{\underline{\sf{\maltese\:\:To\:Find}}}$

• Perimeter of the tennis court

$\underline{\underline{\sf{\maltese\:\:Answer}}}$

• Perimeter of Rectangle = 18a + 6b

$\underline{\underline{\sf{\maltese\:\:Diagram}}}$

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(1.5,-0.7)(0,4.2){2}{\sf\large (5a + 2b)}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large (4a - b)}\put(-0.5,-0.4){\bf }\put(-0.5,3.2){\bf }\put(5.3,-0.4){\bf }\put(5.3,3.2){\bf }\end{picture}$

$\underline{\underline{\sf{\maltese\:\:Calculations}}}$

• Tennis court is in the shape of a rectangle

Perimeter of Rectangle = 2(Length + Width)

Substitute the values

⇒ Perimeter of Rectangle = 2[(5a + 2b) + (4a + b)]

Remove Parentheses

⇒ Perimeter of Rectangle = 2[5a + 2b + 4a + b]

Group Like Terms

⇒ Perimeter of Rectangle = 2[5a + 4a + 2b + b]

Add Similar Elements : 5a + 4a = 9a

⇒ Perimeter of Rectangle = 2[9a + 2b + b]

Add Similar Elements : 2b + b = 3b

⇒ Perimeter of Rectangle = 2[9a + 3b]

Apply the distributive law : a(b + c) = ab + ac

⇒ Perimeter of Rectangle = 2(9a) + 2(3b)

⇒ Perimeter of Rectangle = 18a + 2(3b)

⇒ Perimeter of Rectangle = 18a + 6b

$\underline{\underline{\sf{\maltese\:\:Additional\:Help}}}$

• If you want to calculate the Area of given Rectangle, Here are the steps to calculate Area :

Area of Rectangle = Length × Width

Substitute the values

⇒ Area of Rectangle = (5a + 2b) × (4a + b)

Apply FOIL Method : (a + b)(c + d) = ac + ad + bc + bd

⇒ Area of Rectangle = (5a × 4a) + (5a × -b) + (2b × 4a) + (2b × -b)

⇒ Area of Rectangle = (20a²) + (-5ab) + (8ab) + (-2b²)

⇒ Area of Rectangle = 20a² - 5ab + 8ab - 2b²

⇒ Area of Rectangle = 20a² + 3ab - 2b²

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Answer 2

$\boxed{\bold{\large{Answer \: : }}}$

Perimeter of rectanglular tennis court is 18a + 2b.

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$\boxed{\bold{\large{Step-by-step \: explanation \: : }}}$

${\underline{\bold{Question \: :}}}$

A rectangular tennis court has a length of (5a + 2b) metres, and a width of (4a – b) metres.

Answer the following questions by showing all the working.

(a) Find the perimeter of the tennis court with respect to a and b.

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${\underline{\bold{Given \: :}}}$

• Length of the rectanglular tennis court = (5a + 2b) metres

• Breadth of the rectanglular tennis court = (4a - b) metres

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${\underline{\bold{To \: Find \: :}}}$

• Perimeter of the tennis court with respect to a and b.

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${\underline{\bold{Concept \: Used \: :}}}$

• Perimeter of any polygon = Length of all the sides of the polygon

• Perimeter of rectangle = 2(Length + Breadth)

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${\underline{\bold{Diagram \: :}}}$

Please see the attached image.

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${\underline{\bold{Solution \: :}}}$

Shape of tennis court = Rectangle

So , we need to use the formula of Perimeter of rectangle.

Perimeter of Rectangle = $\bold{2(Length \: + \: Breadth)}$

Perimeter of Rectangle = 2[(5a + 2b) + (4a - b)]

Perimeter of Rectangle = 2[2a + 2b + 4a - b]

Perimeter of Rectangle = 2[5a + 4a + 2b - b]

Perimeter of Rectangle = 2(9a + b)

Perimeter of rectangle = 18a + 2b

∴ Perimeter of rectanglular tennis court is 18a + 2b.

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${\underline{\bold{Answer \: :}}}$

Perimeter of rectangle = 18a + 2b

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${\underline{\bold{Additional \: Information \: :}}}$

• Perimeter of any polygon = Length of all the sides of the polygon

• Perimeter of rectangle = 2(Length + Breadth)

• Perimeter of square = 4 × Side

• Perimeter of triangle = 3 × Side