CAT Exam Model Paper 4 with solutions for free online practice

Question : 23 of 60

Marks: +1, -0

ABCD is a rectangle with BC = a units and DC =

√3

a units. The perpendicular dropped from point A meets BD at point F. The diagonals AC and BD intersect at point G. What is the area (in square units) of ∆AFG?

${√ { 3 } a ^ { 2 } }/ { 12 }$
${ √ { 3 } a ^ { 2 } } /{ 6 }$
${ √ { 3 } a ^ { 2 } } /{ 10 }$
${ √ { 3 } a ^ { 2 } } /{ 8 }$

Validate

Solution:

By Pythagoras theorem:

A C = √{ A B ^ { 2 } + B C ^ { 2 } } = 2 a

Since diagonals of a rectangle are equal and bisect each other:
AG = DG =

{\AC/2}

= a
Hence, ∆DGA is equilateral and since AF is perpendicular to the base DG we can say that AF must divide ∆DGA into two equal halves.
Area of equilateral ∆DGA =

√3/4a^2

square units
square units ∆AFG =

1/2(√3/4a^2)=√3/8a^2

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