Question : Two isosceles triangles have equal vertical angles and their areas are in the ratio 9 :16. Then the ratio of their corresponding heights is:
Option 1: 4.5 : 8
Option 2: 4 : 3
Option 3: 8 : 4.5
Option 4: 3 : 4
Correct Answer: 3 : 4
Solution :
Given, that the Ratio of areas of two isosceles triangles is 9 : 16.
Two isosceles triangles have equal vertical angles.
By angle sum property and equal base angles of the isosceles triangle, the given triangles have angles of the same measure.
So, the triangles are similar to each other by AAA criterion.
Also, we know, the ratio of area of similar triangles is the square of the ratio of heights of similar triangles.
So, (ratio of heights)
2
= 9 : 16
⇒ (ratio of heights) = 3 : 4
Hence, the correct answer is 3 : 4.
Related Questions
Know More about
Staff Selection Commission Sub Inspector ...
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Get Updates Brochure
Your Staff Selection Commission Sub Inspector Exam brochure has been successfully mailed to your registered email id “”.
