# Quadratic Equation Word Question

• Jan 23rd 2010, 03:24 PM
Frankasd
Quadratic Equation Word Question
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 PM
VonNemo19
Quote:

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 $x$ represent the width of the frame. So, how can we represent the area of the frame?
• Jan 23rd 2010, 04:28 PM
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?
• Jan 23rd 2010, 04:59 PM
VonNemo19
Quote:

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 $50cm^2$ , then this implies that the surface area of the frame is $25cm^3$.

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

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

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

What this implies is that, $A_{total}=75cm^2=(10+2x)(5+2x)$, where $x$ is the width of the frame.
• Jan 24th 2010, 05:03 AM
HallsofIvy
Quote:

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 $75^2$. Your equation is (5+2x)(10+2x)= 75. Solve that quadratic equation.