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The line y = b-x with 0 < b < 4 intersects the y-axis at P and the line x= 4 at S. If the ratio of the area of triangle QRS to the area of triangle QOP is 9:16, what is the value of b? Express the answer as a decimal to the nearest tenth.

 

 Jun 18, 2021
 #1
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Triangles QRS   and  QOP   are similar

 

Since  the  areas are in a ratio of 9/16   the scale  factor  of  QRS to QOP  =  3/4 

 

Therefore    Q  =  ( [ 4 / ( 4+ 3)]   * 4  , 0  )    =   [ (4/7) * 4, 0  ]    =     (16/7,  0) 

 

So....since   Q  is on    y  =  b -x

 

Then

 

0   =  b  - (16/7)

 

b   =  16/7

 

cool cool cool

 Jun 18, 2021

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