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The combined area of the 3 windowpanes and frame shown below is 924 inches squared. The frame is of uniform width. What is the side length, x, of each square windowpane?

The combined area of the 3 windowpanes and frame shown below is 924 inches squared The frame is of uniform width What is the side length x of each square window class=

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Answer:

The sides length x of each square windowpane is [tex]10\ in[/tex]

Step-by-step explanation:

we know that

[tex]924\ in^{2}=(6+3x+6)(6+x+6)\\ \\924=(12+3x)(12+x)\\ \\924=144+12x+36x+3x^{2}\\ \\ 3x^{2}+48x- 780=0[/tex]

Solve the quadratic equation

using a graphing tool

The solution is [tex]x=10\ in[/tex]

see the attached figure

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Answer:

10 inches is the side length of each square windowpane.

Step-by-step explanation:

Length of the single window plane = x

Width of the single window plane = x

On combining all the windows pane ,length becomes , l= 3x

On combining all the windows pane ,width becomes , b= x

Length of the frame = L = 6 + 3x+ 6 = 12 + 3x

Width of the frame = B = 6 + x+ 6 = 12 + x

Area of the frame, A = L × B = [tex](12+3x)\times (12+x)[/tex]

Given sum of combined area of the 3 windowpanes and frame = [tex]924 inch^2[/tex]

[tex]a + A=924[/tex]

[tex](12+3x)\times (12+x)=924[/tex]

[tex]144+48x+3x^2=924[/tex]

[tex]3x^2+48x-780=[/tex]

[tex]x^2+16x-260=0[/tex]

[tex]x^2+26x-10x-260=0[/tex]

[tex]x(x+26)-10(x+26)=0[/tex]

[tex](x+260)(x-10)=0[/tex]

x = 10 (accept)

x  = -26 (reject)

10 inches is the side length of each square windowpane.

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