Question

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 25 cm and by 20 cm?
PLEASE SHOW WORK WITH ANSWER, PLEASE!!!!!!!!!

Answer 1

Given dimension of photograph = 25cm * 20cm

So area of photograph = 500cm²

Now, let the width of frame border be = x

So, dimensions of photograph + frame= (25 + 2x)*(20 + 2x)

As given, the area of frame is same as photograph , so

Area of picture + frame = 1000cm  ²

Hence, area equals

$4x^{2}+90x+500=1000$

$4x^{2}+90x-500=0$

$2x^{2}+45x-250=0$

Solving this quadratic equation,

For the quadratic equation of the form $ax^{2}+bx+c=0$ , solution is:

x1,2 = $\frac{-b+\sqrt{b^{2}-4ac}}{2a}$

Now putting a=2, b=45, c= -250 and solving he above equation, we get two values of x.

x = -27.11 (discard it as it is negative)   and

x = 4.61 cm

Hence the dimensions of the frame are:

20+2x = 20+2(4.61) = 29.22 cm

25+2x = 25+2(4.61) = 34.22 cm