Question

Mario is constructing a frame for a 10 inch by 8 inch photo. He wants the frame to be the same width all the way around and the total area of the frame and photo to be 120 square inches. What is the dimension of the frame?

Answer 1

The dimension of the frame are
`(10\ in)by(12\ in)`

Explanation:

Let

x-----> the width of the frame

we know that

`(2x+8)(2x+10)=120` ----> equation that represent the situation

`(2x+8)(2x+10)=120\\ \\4x^(2)+20x+16x+80=120\\ \\4x^(2)+36x-40=0`

Using a graphing tool to solve the quadratic equation

The solution is
`x=1\ in`

see the attached figure

therefore

The dimension of the frame are

`(2(1)+8)*(2(1)+10)`

`(10\ in)*(12\ in)`