Question

A 9-by-12 rectangular picture is framed by a border of uniform width. Given that the combined area of picture plus frame is 180 square units, find the width of the border. show work

Answer 1

The width of the border is 1.5 units

Explanation:

Let

x -----> the width of the border

we know that

The combined area of picture plus frame is 180 square units

so

`180=(9+2x)(12+2x)`

Apply distributive property

`180=(9+2x)(12+2x)\\\\180=108+18x+24x+4x^(2) \\\\4x^(2)+42x-72=0`

Solve the quadratic equation by graphing

using a graphing tool

the solution is x=1.5 units

Remember that the width cannot be a negative number

see the attached figure