Question

Pls answer Q. 60.

Qualitative answer needed.
Pls answer .
Need good explanation.

Answer 1

Answer:

(4) (2 - √2) : 2

Step-by-step explanation:

ΔADE is similar to ΔABC

Since DE cuts the triangle ΔABC into two equal parts

⇒ΔADE : ΔABC = 1  : 2

Applying the property of similar figure:

(Length1/Length2)² = (Area1/Area2)

(AE/AB)² = (ΔADE/ΔABC)

(AE/AB)² = 1/2

AE/AB = √(1/2)

AE/AB = 1/√2

FInd BD:

AE : AB = 1 : √2

BD = AB - AE

BD =√2 - 1

Find BD/AB:

BD/AB = (√2 - 1)/√2

Rationalise the denominator:

BD/AB = (√2 - 1)/√2 x √2/√2

BD/AB = √2(√2 - 1)/2

BD/AB = (2 - √2)/2

Answer: The ratio is  (2 - √2) : 2 (option 4)

Answer 2

Answer:

(4) (2 - √2) : 2