Question

two isosceles triangles have equal vertical angles and their areas are in the ratio 9: 16. find the ratio of their corresponding heights.​

Answer 1

hello mate here's your answer

=> Given ABC and DEF are isosceles triangles and AP and DQ are their respective altitudes or heights. In ΔABC, AB = AC In ΔDEF, DE = DF Also ∠A = ∠D

So, in ΔABC and ΔDEF AB/DE = AC/DF and (angle) A = (angle) D

So by SAS similarity criterion ΔABC::

=> ar(ΔABC)/ar(ΔDEF)=AP^2/DQ^2

=> 9/16 = AP^2/DQ^2

=> AP/DQ = √9/√16

=> AP/DQ = 3/4

AP:DQ = 3:4

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Answer 2

well the following answer is the required answer

See the attachment for further information

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