Question

if 2 similar triangles have ratio of their areas as 27 is to 48 then the ratio of their median is

Answer 1

Answer:

9 : 16

Step-by-step explanation:

as the triangles are similar then there sides will be similar by cpst (corresponding parts of similar triangle )

therefore : if we take the first triangle as tri ABC

and another as tri PQR the the sides

AB ~ PQ ,BC~ QR, AC ~ PR THEN IT IS ALSO PROVE THAT MEDIAN IS ALSO SIMILAR

so ,

construction : join AD as it's median and join PS as it's median

THEN IT IS ALSO PROVE THAT MEDIAN IS ALSO SIMILAR

ar (Tri ABC ) /ar( Tri PQR) = 27/48

1/2 × BC ×AD / 1/2 × QR × PS = 27/48

as all sides of similar triangle are proportional therefore

1 = 27 / 48

1 = 9/ 16

9 : 16 is the ratio of the median