^{2 }- 2x

^{2}-2x -35 = 0

Sarah F.

asked • 12/22/14I need help with this word problem. It's crunch time.

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Hi Sarah,

Ok

let Length = x

then width = x -2 (2 inches less than length

now

A = Lw

35 = x (x -2)

35 = x^{2 }- 2x

x^{2} -2x -35 = 0

(x-7)(x+5) = 0

x-7=0

x=7 (we won't use the other factor since it would give us a negative length

so length = 7

width = 7 -2 = 5

Hope this helps

Moise D. answered • 12/22/14

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New to Wyzant
Patient and Courageous Tutor in Math and Related Subjects

Hi,

Here you have to make sure you interpret the problem correctly.

There is Width and Length of a rectangle, and the width is 2 inches less than the length of a rectangle. This implies that you can assign an unknown letter, X, to be the length and hence the width will be (X-2) which is exactly what's stated in the problem..

Using the formula for the area of rectangle, Area= (width)*(length), in this case Area = (X-2)*(X), since its area is given and it is 35 square inches, helps you to find the unknown

This leads you to solving the equation (X-2)(X)=35 => X^{2}-2X-35=0... This is a quadratic expression that may have to real values, after solving, keep the one that makes sense.

Antoinette W. answered • 12/22/14

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Caring, Effective Tutor- Math, Reading, Test Prep, Sports Conditioning

width = "width is" means w = "2 inches less" means subtract 2 "than" [switch first and last] "its length" means l= l - 2

Area = 35 in 2

Area of a rectangle = (l)(w)

Substitute

A = (l)(l-2)

35 = (l)(l-2)

Distribute/Multiply

35 = l2 - 2l

Balance

l2 - 2l - 35 = 0

Factor

(l - 7)(l + 5) = 0

Solve (set each factor = to 0)

This will lead you to find the length

Re-read question to find the phrase that will help you find the width

Let X = the length; then the width = X - 2

the Area of a rectangle = L x W = X(X - 2)

since the area = 35cm^{2}, we write 35cm^{2} = X(X - 2)

expanding this equation, 35cm2 = X2 - 2X

rewriting, 0 = X2 - 2X -35cm^{2}

factoring, 0 = (X - 5cm)(X + 7cm)

so the two roots are -5 and +7, but since no length can equal a minus number, we can discard that root

which leaves us with +7cm, thus X - 2 = +5cm

so, the length = +7cm, and the width = +5cm

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