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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?
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Respuesta :

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

[tex]4x^{2}+90x+500=1000[/tex]

[tex]4x^{2}+90x-500=0[/tex]

[tex]2x^{2}+45x-250=0[/tex]

Solving this quadratic equation,

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

x1,2 = [tex]\frac{-b+\sqrt{b^{2}-4ac}}{2a}[/tex]

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



raphealnwobi

The width of the frame border is 4.61 cm.

What is an area

Area is the amount of space occupied by a two dimensional object or figure. For a rectangle:

Area = length * width

The length of the photograph be 25 cm and the width is 20 cm, hence:

Area = 20 * 25 = 500 cm²

Since the border is uniform, let w be the width hence:

500 + 500 = (25 + 2w)(20 + 2w)

w = 4.61 cm

The width of the frame border is 4.61 cm.

Find out more on area at: https://brainly.com/question/19819849

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