ValentinaT
Help with geometry/rational expressions?



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ValentinaT
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hea
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1st step: What is the area of the rectangle?

ValentinaT
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\[\frac{ 1 }{ 6 }? \]

ValentinaT
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If you cut the triangle in half, and then stack it on top of the other, and divide up the rectangle, it could be \[\frac{ 1 }{ 6 }\]

hea
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I'm just asking for the total area of the rectangle for now. The sides of the rectangle are x and x+2. So what is the area?

ValentinaT
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(x)(x + 2)

hea
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Great, now we try to find the area of the triangle. Any ideas?

ValentinaT
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(x)(2)

hea
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dw:1367591002545:dw

ValentinaT
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(2)(x/2)

ValentinaT
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(Two times x divided by two.)

hea
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Well that happens to be the area of the total triangle which is great! So now to get the fraction we can write\[{areaOfTriangle\over TotalArea}\]

hea
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\[{x\over(x)(x+2)}\]x's cancel.

ValentinaT
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Oh, okay.

hea
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Does that make sense? Did you understand?

ValentinaT
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I think I might.
dw:1367591373451:dw

hea
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\[{1\over x+2}\]

ValentinaT
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The fraction for the triangle is \[\frac{ 1 }{ x + 2 }\]
Yes?

hea
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That is the answer to the question, yes

ValentinaT
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For the fraction of the rectangle shaded?

hea
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yes

ValentinaT
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Thank you!