Given CS=2x+1, SB=6x, CR=7.5, and RA=18. What must the value of x be in order to prove SR || BA? Justify your answer
1 answer:
In the image provided
, we understand that
in similar triangles, the ratio of the lengths of sides CS and CB should equal the ratio of CR to CA. Thus, we have CS / CB = CR / CA
, which can be expressed as
CS / (CS + SB) = CR / (CR + RA)
. By cross-multiplying we arrive at
CS*(CR+RA) = CR*(CS+RA)
. We know that CS = 2x+1
and SB = 6x
, while CR = 7.5
and RA = 18
. Therefore, substituting gives us
(2x + 1)*[7.5 + 18] = 7.5*[2x + 1 + 18]
. Thus
, (2x + 1)*[25.5] = 7.5*[2x + 19]
. This leads to the equation
(51x + 25.5) = 15x + 142.5
. From here, we simplify
51x - 15x = 142.5 - 25.5 which results in36x = 117
. Hence, we findx = 117/36 and finally
x = 3.25
.
, we understand that
in similar triangles, the ratio of the lengths of sides CS and CB should equal the ratio of CR to CA. Thus, we have CS / CB = CR / CA
, which can be expressed as
CS / (CS + SB) = CR / (CR + RA)
. By cross-multiplying we arrive at
CS*(CR+RA) = CR*(CS+RA)
. We know that CS = 2x+1
and SB = 6x
, while CR = 7.5
and RA = 18
. Therefore, substituting gives us
(2x + 1)*[7.5 + 18] = 7.5*[2x + 1 + 18]
. Thus
, (2x + 1)*[25.5] = 7.5*[2x + 19]
. This leads to the equation
(51x + 25.5) = 15x + 142.5
. From here, we simplify
51x - 15x = 142.5 - 25.5 which results in36x = 117
. Hence, we findx = 117/36 and finally
x = 3.25
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