Marvin wants to purchase a rectangular rug. it has an area of 80 square feet. he cannot remember the length and width, but he remembers that the length was 8 more than some number and the width was 8 less than that same number. write a quadratic equation using the information given.

Let 'some number' be 'x'.

L = length = x + 8

W = width = x + 8

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The transitive property teaches that if a=b and b=c, then a=c.

Therefore, L = W.

That means the rug is square.

Of course, a square is an equilateral rectangle, so that is okay.

.

A = area = L*W = L^2 = W^2 = 80 sq. ft.

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L = sqrt(80) = sqrt(16*5) = sqrt(16)*sqrt(5) = 4*sqrt(5) = 8.94427191

.

So L = W = 8.94427191

.

Returning to the setup, L = x+8 = 8 + .94427191.

So x = .94427191

No wonder he could not remember it.

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Step-by-step explanation:

80 times x divide by 8

Step-by-step explanation: you don't know what the length is but you do know what the width is

no association

step-by-step explanation:

if you have eyes and you can use them efficiently you can see that it just looks like random dots like do a line of best fit and like they're so spread out it's such a weak association you might as well consider it nonexistent

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4