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# Please help i have no idea what to do! Any help appreciated even if I don't know what it means

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In the figure below, a 3-inch by 3-inch square adjoins a 10-inch by 10-inch square. What is the area of the shaded region? Express your answer in square inches as a common fraction. Mar 9, 2022

#1
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The area of the shaded region is 11/2.

Mar 9, 2022
#2
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The slope of the line is -10/13. Multiply this by 10, and this means the line goes down -100/13 out of -130/13. This also means the line goes down 30/13 in the smaller square, meaning the area is:

$$9 - ({30 \over13} \times {3 \over 2}) = \color{brown}\boxed{72 \over 13}$$

Mar 9, 2022
#5
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Can you explain, -10/13 as the slope? Oh wait, nevermind

edited by PikachuLovesKetchup  Mar 9, 2022
#3
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Another method

Note  that  triangles   ABD  and  FGD are similar

Call   DG  = x        BD   =   10  - x         AB  =10    and    FG  = 3

So.....by  similar triangles

DG /  BD  =   FG  /AB

x / ( 10 - x)  =  3  / 10          cross-multiply

10x =  3 ( 10 - x)

10x  = 30  - 3x

13x = 30

x = 30 /13

The area of triangle   FGD   =  (1/2) (FG) ( DG)  = (1/2) (3) (30/13) =  90 / 26  =  45/13

So the shaded  area   =   [ CEFG ]  - [ FGD ]   =   9 - 45 /13   = 72 / 13  [ as BuilderBoi found !!! ]   Mar 9, 2022
#6
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Cool, thanks!

#4
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Thanks guys! I appreciate it!

Mar 9, 2022