Question

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?

Answer 1

10 inches is the side length of each square windowpane.

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)* (12+x)`

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

`a + A=924`

`(12+3x)* (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.

Answer 2

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

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