Question

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Answer 1

Answer:

OPTION C

Step-by-step explanation:

GIVEN:

A rectangle ABCD, AB= 5 unit, BC = 3 unit, DF = 1 unit, GC = 2 units, So FG = 2 units.

DC // AB , ie, FG // AB

TO FIND : Atea triangle AEB

Since, triangle EFG ~ triangle EAB ( by AAA similarity criterion)

So, ratio of the areas of 2 similar triangles is equal to the squares of the ratio of their corresponding sides

So, area ( triangle EFG) / area( triangle EAB) = FG² / AB² = 4/ 25

So, area ( trapezium ABGF) = 25x - 4x= 21x ……….(1)

Now, we can also calculate, area( trap ABGF) = ar{( rect ABCD)} - {( ar( tri BCG) + ar( tri ADF)}

=> area( teap ABGF) * 15 - ( 3 + 3/2)

= 15 - 9/2

=> 21//2 ………….(2)

Eq(1) = Eq (2)

21x = 21/2

=> x = 21/42 = 1/2

So, x = 1/2

So, area( triangle AEB) = 25 x = 25 x = 25/2 = 12.5 square unit..