in the given figure,P is a point on side BC of triangle ABC such that BP:PC=1:2 and Q is a point on AP such that PQ :QA=2:3 .show that area of triangle AQC :area of triangle ABC=2:5 in the given figure,P is a point on side BC of triangle ABC such that BP:PC=1:2 and Q is a point on AP such that PQ :QA=2:3 .show that area of triangle AQC :area of triangle ABC=2:5
Dear Student,
Please find below the solution to the asked query:
Given : BP : PC = 1 : 2 , Let ratio coefficient = x , So BP = x and PC = 2 x , Then , BC = BP + PC = x + 2 x = 3 x
Let height = h1 with corresponding base is ' BC ' .
We know area of triangle = , So
Area of ABC =
And
Area of APC =
Then ,
Also given : PQ : QA = 2 : 3 , Let ratio coefficient = y , So PQ = 2 y and QA = 3 y , Then , AP = PQ + QA = 2 y + 3 y = 5 y
Let height = h2 with corresponding base is ' AP ' .
Then
Area of APC =
And
Area of AQC =
Then ,
Substitute that value in equation 1 we get
Hope this information will clear your doubts about topic.
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards
Please find below the solution to the asked query:
Given : BP : PC = 1 : 2 , Let ratio coefficient = x , So BP = x and PC = 2 x , Then , BC = BP + PC = x + 2 x = 3 x
Let height = h1 with corresponding base is ' BC ' .
We know area of triangle = , So
Area of ABC =
And
Area of APC =
Then ,
Also given : PQ : QA = 2 : 3 , Let ratio coefficient = y , So PQ = 2 y and QA = 3 y , Then , AP = PQ + QA = 2 y + 3 y = 5 y
Let height = h2 with corresponding base is ' AP ' .
Then
Area of APC =
And
Area of AQC =
Then ,
Substitute that value in equation 1 we get
Hope this information will clear your doubts about topic.
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.
Regards