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A quadrilateral has two pairs of congruent sides and a longer diagonal of length 6, as shown. For what value of x will the area of the shaded area be 40% of the area of the unshaded region?  

 May 1, 2019
 #1
avatar+10603 
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A quadrilateral has two pairs of congruent sides and a longer diagonal of length 6, as shown. For what value of x will the area of the shaded area be 40% of the area of the unshaded region?  

laugh

 May 2, 2019
 #2
avatar+104648 
+2

We only need to look at the top  two triangles.....they are under the same height.....and the areas of triangles under the same height are to each other as their bases

 

So.......

 

x / (6 - x)  = .40      cross-multiply

 

x =  .40 (6 - x)

 

x = 2.4 - .4x       

 

1.4x  = 2.4       

 

x = 2.4/1.4  =   12/7

 

Proof :   [ 2*  area of triangle on the left ] /  [ 2 * area of triangle on the right ]  =   

 

[ 2 * triangle height * base length of left triangle ]  / [ 2 * triangle height * base length of right triangle ] =  

 

[ base length of triangle on the left ]  / [ base length of triangle on the right ]

 

[12/ 7 ] / [ 6 - 12/7 ]   =

 

[ 12/7 ] / [ 42/7 - 12/7 ]  =

 

[12/7 ] / [ 30/7]   =

 

[ 12/7] * [ 7/30 ]  =

 

12/30  =

 

4/10   =

 

.40  = 40%

 

 

cool cool cool

 May 2, 2019

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