SSC MTS Model Paper 6

Question : 39 of 150

Marks: +1, -0

The ratio of the area of the equilateral triangle described on the side of a square to the area of the equilateral triangle described on its diagonal is:

1 : 3
3 : 4
1 : 2
1 : 4

Validate

Solution:

Here

{ AC } ^ { 2 } = 2 { AB } ^ { 2 }

As ∆ABE and ∆ABC are equiangular so ∆ABE ~ ∆ABC
[The ratio of the areas of two similar triangles is equal to the ratio of the square of their correspondingsides]

{ { area of } ( ∆ { ABE } ) } /{ { area of } ( ∆ { ACF } ) } = { { AB } ^ { 2 } } /{ { AC } ^ { 2 } } = { { AB } ^ { 2 } } /{ 2 { AB } ^ { 2 } } = { 1 } /{ 2 }

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