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lukranit [14]
3 years ago
13

The combined area of the 3 windowpanes and frame shown below is 924 inches squared. The frame is of uniform width. What is the s

ide length, x, of each square windowpane?

Mathematics
2 answers:
Maslowich3 years ago
7 0

Answer:

The sides length x of each square windowpane is 10\ in

Step-by-step explanation:

we know that

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

Solve the quadratic equation

using a graphing tool

The solution is x=10\ in

see the attached figure

Zinaida [17]3 years ago
3 0

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 = (12+3x)\times (12+x)

Given sum of combined area of the 3 windowpanes and frame = 924 inch^2

a + A=924

(12+3x)\times (12+x)=924

144+48x+3x^2=924

3x^2+48x-780=

x^2+16x-260=0

x^2+26x-10x-260=0

x(x+26)-10(x+26)=0

(x+260)(x-10)=0

x = 10 (accept)

x  = -26 (reject)

10 inches is the side length of each square windowpane.

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