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The area in square feet of a rectangular field is x^2-160x+6300. The width, in feet, is x-70. What is the length in feet?

Would really appreciate if you explain, I need to know this for my final!

Respuesta :

cuddlydva
To find the answer, it is best to use formulas.  Area is mentioned, so lets use the formula for area, A=lw. Plugging in, you get [tex] x^{2} -160x+6300=l(x-70)[/tex] .  While this might look confusing, it is easier than you think: divide both sides by (x-70) for [tex]l= \frac{x^{2}-160x+6300 }{x-70} [/tex] .  From here, try factoring the top: there is a -90 difference between -70 and -160 and luckily -70 times -90 equals 6300.  So, your equation should look like [tex]l= \frac{(x-70)(x-90)}{(x-70)} [/tex] .  You can eliminate (x-70) from the top and bottom, so you should get l=x-90 .  Since there is no way to find x, x-90 is your length.

The value of the length of the rectangular field is x-90 feet.

The area of a rectangle is calculated as: = Length × Width

Based on the information given, the area of the rectangular field is x² - 160x + 6300 and the width, in feet, is x-70.

Therefore, the length will be:

Length = Area / Width

Length = (x² - 160x + 6300) / (x-70)

Length = x-90

The value of the length of the rectangular field is x-90 feet.

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