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The area of a rectangle is 24 square centimeters. The length (), in centimeters of the rectangle is given by the equation + 5x = 24. What is the length of the rectangle? ОА 3 cm O B. 5 cm OC 8 cm OD. 12 cm

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ANSWER

[tex]A.3\operatorname{cm}[/tex]

EXPLANATION

The area of the rectangle is given as 24 sq cm and the length, x, is given as:

[tex]x^2+5x=24[/tex]

To find the length of the rectangle, x, solve the equation by factorization.

That is:

[tex]\begin{gathered} x^2+5x-24=0 \\ x^2+8x-3x-24=0 \\ x(x+8)-3(x+8)=0 \\ (x-3)(x+8)=0 \\ \Rightarrow x=3;x=-8 \end{gathered}[/tex]

Since the length of a rectangle cannot be negative, the correct answer is:

[tex]A.3\operatorname{cm}[/tex]