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?

2. Originally Posted by Frankasd
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?
Let $\displaystyle x$ represent the width of the frame. So, how can we represent the area of the frame?

3. 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?

4. Originally Posted by Frankasd
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?
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.

5. Originally Posted by Frankasd
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?
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.