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Math Help - Quadratic Equation Word Question

  1. #1
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    Quadratic 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?
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Frankasd View Post
    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?
    Let x represent the width of the frame. So, how can we represent the area of the frame?
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  3. #3
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    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?
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  4. #4
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Frankasd View Post
    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.
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  5. #5
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    Quote Originally Posted by Frankasd View Post
    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.
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