Question

if a point d divides line segment ab of length 10cm internally in the ratio 2:3, then find the length of AD

Answer 1

Question :- if a point ‘D’ divide line segment AB of length 10cm internally in the ratio 2:3 then find the length of AD ?

Answer :-

Let us assume that, D divide the line segment AB in ratio of 2x and 3x respectively .

so,

→ AD + DB = 2x + 3x

→ AB = 5x

→ 10 = 5x

→ x = 2 cm

therefore,

→ AD = 2x

→ AD = 2 * 2 = 4 cm. (Ans.)

Hence, Length of AD will be 4 cm.

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Answer 2

SOLUTION

GIVEN

A point ‘D’ divide line segment AB of length 10cm internally in the ratio 2:3

TO DETERMINE

The length of AD

EVALUATION

Here it is given that a point ‘D’ divide line segment AB of length 10cm internally in the ratio 2:3

So the given ratio is 2 : 3

$\displaystyle \sf{ \therefore \: \: Share \: of \: AD \: = \frac{2}{2 + 3} = \frac{2}{5} }$

$\displaystyle \sf{ \therefore \: \: Share \: of \: BD \: = \frac{3}{2 + 3} = \frac{3}{5} }$

Hence

$\displaystyle \sf{ \therefore \: \: Length\: of \: AD \: = 10 \times \frac{2}{5} \: cm= 4 \: cm}$

$\displaystyle \sf{ \therefore \: \: Length\: of \: BD \: = 10 \times \frac{3}{5} \: cm= 6 \: cm}$

FINAL ANSWER

The length of AD = 4 cm

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