What will be the ratios of areas of similar ∆ABC and ∆PQR, if the altitudes of the triangles are 10cm and 5.5cm respectively?(a) 150 : 4(b) 300 : 7(c) 100 : 3(d) 400 : 9The question was asked during an online exam.The query is from Area of Similar Triangle topic in chapter Triangles of Mathematics – Class 10

What will be the ratios of areas of similar ∆ABC and ∆PQR, if the

1.	What will be the ratios of areas of similar ∆ABC and ∆PQR, if the altitudes of the triangles are 10cm and 5.5cm respectively?(a) 150 : 4(b) 300 : 7(c) 100 : 3(d) 400 : 9The question was asked during an online exam.The query is from Area of Similar Triangle topic in chapter Triangles of Mathematics – Class 10
Answer» The CORRECT answer is (d) 400 : 9 For explanation I would say: We know that the ratio of areas of SIMILAR triangles is EQUAL to the ratio of the squares of their corresponding altitudes. Here, AD = 10cm and PS = 5.5 cm According to the theorem, \(\frac {area \, of \, \triangle ABC}{area \, of \, \triangle PQR}=(\frac {AD}{PS})\)^2 \(\frac {area \, of \, \triangle ABC}{area \, of \, \triangle PQR}=(\frac {10}{5.5})\)^2 \(\frac {area \, of \, \triangle ABC}{area \, of \, \triangle PQR}=\frac {100}{2.25}=\frac {400}{9}\)

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