Question

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

Answer 1

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

Answer 2

The answer is the option A

`0.5\ ft`

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`