Respuesta :

so first off, remember the formula for the area of a rectangle. it's length time width right? or, you could think that A= 2 things multiplied together. how can we simplify x^2 - x -72 to equal two things multiplied together? well, we can factor it! We know that one of the factors is x+8 right? so what's the other factor? it would be x-9. so, we know width is x-9. I'm not sure if you need an actual value for width. if so, I could probably go further.
aachen

Answer:

[tex]w=x-9[/tex]

Step-by-step explanation:

It is given that area of the rectangle is [tex]\left (x^{2} -x-72\right )\:m^{2}[/tex] and length of the rectangle is [tex](x+8) \:m[/tex]

We know that area of rectangle is length[tex]\times[/tex]width

We have, [tex]l\times b=x^{2}-x-72[/tex]

[tex]w=\frac{x^{2}-x-72}{x+8} \:\:\left [ \because l=x+8 \right ][/tex]

[tex]w=\frac{x^{2}-9x+8x-72}{x+8}[/tex]

[tex]w=\frac{x\left ( x-9 \right )+8\left ( x-9 \right )}{x+8}[/tex]

[tex]w=\frac{\left ( x+8 \right )\left ( x-9 \right )}{x+8}[/tex]

[tex]w=x-9[/tex]

Hence, width of the rectangle is [tex]w=(x-9)\,m[/tex]

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