Hello could someone please help me with this?

A picture measuring 5cm by 10cm is surrounded by a frame with half the area of the picture. The width of the frame is to be the same on all sides. What is the frame's thickness?

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- Jan 23rd 2010, 04:24 PMFrankasdQuadratic Equation Word Question
Hello could someone please help me with this?

A picture measuring 5cm by 10cm is surrounded by a frame with half the area of the picture. The width of the frame is to be the same on all sides. What is the frame's thickness? - Jan 23rd 2010, 04:40 PMVonNemo19
- Jan 23rd 2010, 05:28 PMFrankasd
Let x represents the width of the frame

xl=Area of picture=50

xl=Area of the frame=25

(5+x)(10+x)=75^2? - Jan 23rd 2010, 05:59 PMVonNemo19
Well, let's see...If the surface area of the is , then this implies that the surface area of the frame is .

Now note that the length of the entire picture - including the frame - is .

Likewise, the width is . (the 2 accounts for both sides of the picture)

Also, note that the total surface area is

What this implies is that, , where is the width of the frame. - Jan 24th 2010, 06:03 AMHallsofIvy
Two errors. first, the frame is on

**both**top and bottom so the "height" would be 10+ 2x, not 10+ x and the**two**sides of the frame make the total "width" 5+ 2x, not 5+ x.

Second, the product, (5+ 2x)(10+ 2x) is the total area, 50+ 25= 75, not . Your equation is (5+2x)(10+2x)= 75. Solve that quadratic equation.