A rectangular stained glass window is 2 feet by 4 feet. A clear glass border is constructed around the stained glass window. the width of the border is equal and was made out of 7 square feet of clear glass. What is the width of the border? A. 0.5ft B. 1.5 ft C. 2.5 ft D. 3.5 ft

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Alina87 Alina87 · Answer 1 · 2016-03-13T04:12:03-04:00

S=2(4x+2x)+4x^2=
=4x^2+12x

4x^2+12x=7
4x^2+12x-7=0
D=12^2-4×4×(-7)=256
x1=(-12-16)/(2×4)=-3,5 (impossible)
x2=(-12+16)/(2×4)=0,5

A

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calculista calculista · Answer 2 · 2018-12-29T17:19:17-05:00

Answer:

The answer is the option A

\(0.5\ ft\)

Step-by-step explanation:

Let

x-------> the width of the border

we know that

The total area of the window plus the border is equal to

\(A=2*4+7=15\ ft^{2}\)

\((2+2x)(4+2x)=15\\2*4+2*2x+2x*4+2x*2x=15\\8+4x+8x+4x^{2}=15\\4 x^{2}+12x-7=0\)

Using a graphing tool -----> to resolve the quadratic equation

see the attached figure

The solution is

\(x=0.5\ ft\)

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