a doubles tennis court measures (7x+8) ft in length and (3x+6) ft in width. which expression represents the area of the court

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10-11-2021
Mathematics

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a doubles tennis court measures (7x+8) ft in length and (3x+6) ft in width. which expression represents the area of the court

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akposevictor akposevictor · Answer 1 · 2021-11-17T10:03:15+01:00

If the length of a tennis court is (7x + 8) ft, and its width is (3x + 6) ft, the expression of that represents the area of the court is: [tex]\mathbf{Area = 21x^2 + 66x + 48}[/tex]

Recall:

Area of a rectangle = length x width

Given the algebraic expressions for the dimension of the rectangular court as:

length = (7x + 8) ft

width = (3x + 6) ft

Therefore,

Area = [tex](7x + 8) \times (3x + 6)[/tex]

Apply the distributive property

[tex]Area =7x(3x + 6) +8(3x + 6)\\\\Area = 21x^2 + 42x + 24x + 48\\\\[/tex]

Add like terms

[tex]\mathbf{Area = 21x^2 + 66x + 48}[/tex]

Therefore, if the length of a tennis court is (7x + 8) ft, and its width is (3x + 6) ft, the expression of that represents the area of the court is: [tex]\mathbf{Area = 21x^2 + 66x + 48}[/tex]

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