Question

If AD = 5 and BD = 2, then area of ΔADE : area of trapezium DBCE is equal to ______.

Options

• 5 : 2

• 2 : 5

• 24 : 25

• 25 : 24

Answer 1

If AD = 5 and BD = 2, then area of ΔADE : area of trapezium DBCE is equal to 25 : 24. 

Explanation:

From figure,

In △ ADE and △ ABC,

⇒ ∠DAE = ∠BAC (Common angle)

⇒ ∠ADE = ∠ABC (Corresponding angles are equal)

∴ △ ADE ~ △ ABC (By A.A. postulate)

From figure,

AB = AD + DB = 5 + 2 = 7 cm.

We know that,

The areas of two similar triangles are proportional to the squares on their corresponding sides.

∴ `("Area of"△ ADE)/("Area of" △ ABC) ​= (AD^2)/(AB^2)​`

= `(5^2​)/(7^2)`

= `25​/49`

= 25 : 49

Let area of △ ADE = 25x and area of △ ABC = 49x

From figure,

Area of trapezium DBCE = Area of △ ABC − Area of △ ADE = 49x − 25x = 24x

∴ `("Area of" △ ADE)/("Area of trapezium"  DBCE)​`

= `​(25x)/(24x)​`

= `25/24`

⇒ Area of △ ADE : Area of trapezium DBCE = 25 : 24.