A uniform border on a framed photograph has the same area as the photograph. What are the outside dimensions of the border if the dimensions of the photograph are 25cm by 20cm?

What would a diagram for this question look?

Printable View

- Apr 25th 2010, 11:52 AMsinjid9Help with diagram
A uniform border on a framed photograph has the same area as the photograph. What are the outside dimensions of the border if the dimensions of the photograph are 25cm by 20cm?

What would a diagram for this question look? - Apr 25th 2010, 12:21 PMArchie Meade
Hi sinjid9,

the attachment shows a diagram.

You can either subtract the photo area from the area inside the outer

perimeter of the frame

$\displaystyle (20+2x)(25+2x)-500=500$

or add up the areas inside the border

$\displaystyle 2(25+2x)x+2(20)x=500$

Hence, you must solve

$\displaystyle 2x^2+45x-250=0$

As this doesn't factorise easily, use

$\displaystyle x=\frac{-45\pm\sqrt{45^2-4(2)(-250)}}{2(2)}$

to find x.

You should get a value slightly greater than 4