Geometry Practice Test 1

Question : 8 of 40

Marks: +1, -0

In ΔABC, D and E are points on AB and AC respectively, such that DE || BC and DE divides the ΔABC into two parts of equal areas. The ratio of AD and BD is:

1 : 1
1 : $√2$ − 1
1 : 2
1 : $√2$ +1

Validate

Solution:

Area of triangle ADE = (Area of DEBC)
⇒ Area of DEBC =

1/2

area of ΔABC
So,

{\Area \of Δ \ABC}/{\Area \of Δ \ADE}

2/1

The ratio of the area of two similar triangles is equal to the square of the ratio of their corresponding sides.
So,

({AB}/{AD})^2

2/1

{AB}/{AD}

√2/1

{AD+AB}/{AD}

√2/1

1 +

{BD}/{AD}

√2/1

{BD}/{AD}

√2/1 - 1

{BD}/{AD}

{√2-1}/1

{AD}/{BD}

1/{√2-1}

So, the required ratio = 1 :

√2

- 1

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