Some Simple concepts to solve this tricky Question : ( mug this up )

1. Equilateral Triangle has the largest area of all triangles with same Perimeter.

2. 2a < Perimeter , where a is a side of a Triangle , which basically means that twice of any side of a Triangle cannot be greater than its Perimeter.

Now , coming back to the Question :

Given : Perimeter of both the Triangles = 30.

1. If you want to maximize the area , you will need an Equilateral triangle which makes the side = 10 .

2. If you want to maximize the base , the longest length will be 14 ( because of Rule No. 2 mentioned above ) .

Ratio of these 2 will give you 14/10 = 7:5 ( Answer Option D)

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