+0

i'm confused

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121
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BCDF is a rectangle.  Triangle ABE has area 2.  Triangle BEF has area 3.  Find the area of the blue region.

May 12, 2020

#1
+902
-5

We notice blue+green is half of the rectangle.

Green + yellow is 1/4.

1/4 of the rectangle is 2+3 = 5, so the rectangle is 5*4 = 20.

20/2 = 10, which is half, and -2 for green and the blue is 8.

If you don't understand anything feel free to ask.

May 12, 2020
#2
+1

"If you don't understand anything feel free to ask."

Nice reasoning,  But how do you know that A is the mid-point of CB?

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Guest May 12, 2020
#5
+902
-5

True, but without any other information that's an assumption you must make.

hugomimihu  May 12, 2020
#7
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An incorect assumption !

Guest May 12, 2020
#3
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+1

Let the side lengths of the rectangle BCDF be  3 cm and  5 cm

AB = 3.333333333 cm

EN = 1.2 cm               EM = 2 cm

Area of the blue region is   5.5 cm²

May 12, 2020
edited by Dragan  May 12, 2020
edited by Dragan  May 12, 2020
edited by Dragan  May 12, 2020
edited by Dragan  May 12, 2020
#4
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"Rectangle side lengths are  3 and  5"

How do you know that?  Where did those numbers come from?

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Guest May 12, 2020
#9
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I drew the rectangle with the sides of 5 and 4, and it didn't work.

Eventually, I decreased the shorter side to 3 units, and it worked like a charm.

Dragan  May 12, 2020
#6
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The area of the blue region is 5.5cm2 but it isn't possible to say what the actual lengths of sides are.

All that you can deduce is that their product is 15.

A 3 by 5 rectangle works, but so does, for example, a 1 by 15 or a 7.5 by 2 etc. .

Incidently, A is two thirds of the way along BC not a half.

May 12, 2020
#8
+1322
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See my diagram regarding the lengths of sides of a blue region.

Dragan  May 12, 2020