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, 03:24 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, 03:40 PMVonNemo19
- Jan 23rd 2010, 04:28 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, 04:59 PMVonNemo19
Well, let's see...If the surface area of the is $\displaystyle 50cm^2$ , then this implies that the surface area of the frame is $\displaystyle 25cm^3$.

Now note that the length of the entire picture - including the frame - is $\displaystyle L=10+x+x=10+2x$.

Likewise, the width is $\displaystyle W=5+2x$. (the 2 accounts for both sides of the picture)

Also, note that the total surface area is $\displaystyle A_{total}=50cm^2+25cm^2=75cm^2$

What this implies is that, $\displaystyle A_{total}=75cm^2=(10+2x)(5+2x)$, where $\displaystyle x$ is the width of the frame. - Jan 24th 2010, 05:03 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 $\displaystyle 75^2$. Your equation is (5+2x)(10+2x)= 75. Solve that quadratic equation.