Question

A picture inside a frame is 2 inches longer than it is wide. The picture is in a frame that has a width of 3 inches on each side of the picture. If the area of the picture, including the frame, is 195 inches^2, find the dimensions of the frame.

Answer 1

The dimensions of the frame are 15 in x 13 in

Explanation:

Let

x ----> the length of the picture

y ----> the width of the picture

we know that

`x=2+y` -----> equation A

The area of the picture, including the frame is

`A=(x+6)(y+6)`

`A=195\ in^2`

so

`195=(x+6)(y+6)` ----> equation B

substitute equation A in equation B

`195=(2+y+6)(y+6)`

solve for y

`195=(y+8)(y+6)\\y^2+6y+8y+48=195\\\\y^2+14y-147=0`

solve the quadratic equation by graphing

The solution is y=7 in

see the attached figure

Find the value of x

`x=2+7=9\ in`

Find the dimensions of the frame

`x+6=9+6=15\ in`

`y+6=7+6=13\ in`

therefore

The dimensions of the frame are 15 in x 13 in