If triangle pqr and Triangle pst are similar find the length of rs ? Where QR&ST are parallel line & R=90 Degree, QR=10cm RT=12cm & ST=6CM in a triangle.
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Given:
ST || RQ
PS= 3 cm
SR = 4cm
We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.
ar(∆PST) /ar(∆PRQ)= (PS)²/(PR)²
ar(∆PST) /ar(∆PRQ)= 3²/(PS+SR)²
ar(∆PST) /ar(∆PRQ)= 9/(3+4)²= 9/7²=9/49
Hence, the required ratio ar(∆PST) :ar(∆PRQ)= 9:49
ST || RQ
PS= 3 cm
SR = 4cm
We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.
ar(∆PST) /ar(∆PRQ)= (PS)²/(PR)²
ar(∆PST) /ar(∆PRQ)= 3²/(PS+SR)²
ar(∆PST) /ar(∆PRQ)= 9/(3+4)²= 9/7²=9/49
Hence, the required ratio ar(∆PST) :ar(∆PRQ)= 9:49
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