Question

2. A rectangular photograph measuring 8 in by 10 in is surrounded by a frame with a uniform width, xx.

a. What type of function can best represent the area of the picture and the frame in terms of xx (the unknown frame’s width)? Explain mathematically how you know.
b. Write an equation in standard form representing the area of the picture and the frame. Explain how you arrive at your osition.

Answer 1

Answer: a) Quadratic equation b)
`4x^2+36x+80`

Explanation:

Since we have given that

Length of photograph = 8 inches

Width of photograph = 10 inches

It is surrounded by a frame with uniform width 'x'.

So, Length of picture and frame becomes

`x+8+x=2x+8`

Width of picture and frame becomes

`x+10+x=2x+10`

So, Area of picture and frame becomes

`Length* breadth\\\\=(2x+8)(2x+10)\\\\=2x(2x+10)+8(2x+10)\\\\=4x^2+20x+16x+80\\\\=4x^2+36x+80`

Hence, a) Quadratic equation b)
`4x^2+36x+80`