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What percentage of the square's area is shaded blue?

 

 May 5, 2020
 #1
avatar+1498 
+4

We can eliminate choice 50%, since BD splits the square in half, but the shaded doesn't fill it up.

 

So our answer is less than 50. We remove the right traingle at the bottom which has an area of 4*1/2 = 2. 2/16 = 1/8

 

That's another 12.5%.

 

Oops we missed the small one! We over counted that one.

 

First, 50-12.5 = 37.5, but we need to add that, and the size appears to be 2.5%, since it's a similar triangle of the shaded, but like 16 times smaller

 

also to clarify, the small triangle is probably 2.5% since it's probably no more than a third of the right triangle there, but if it's even 1 third, it would be 4 percent and STILL around 40.

 

I'm very sure it's 40 but it's more of a gut feeling than hard proof.

 May 5, 2020
edited by hugomimihu  May 5, 2020
 #4
avatar+111326 
0

Correct, Hugo...."gut feelings"  are good......except if you're hungry  !!!!

 

 

cool cool cool

CPhill  May 5, 2020
 #5
avatar+1498 
+4

Haha, but mine was more of guesswork and your answer is definitely the best.

hugomimihu  May 5, 2020
 #2
avatar+111326 
+3

Call the intersection of BD   and AQ , M

 

Then triangle BMA  is  similar to  triangle DMQ

 

Since  the base of BMA  is  4 times that of DMQ.....so is its altitude

 

Therefore

 

Altitude BMA  + Altitude  of  DMQ  =   4

 

Alltitude of BMA  + (1/4)Altitude of BMA  = 4

 

(5/4) Altitude BMA  = 4

 

Altitude of BMA = ( 4 *4/5) = 16/5

 

Area of BMA  = (1/2)(4)(16/5)  =  32/5

 

Ara of the square   = 16

 

(32/5)  / 16   =     

 

 

32 / 80  =

 

2 / 5   =

 

40%

 

 

cool cool cool

 May 5, 2020
 #3
avatar+1498 
+6

I'm not going to pretend I know what that means but that looks like good proof there!

hugomimihu  May 5, 2020

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