Question

- In the adjoining figure exterior EAB = 110°,
CAD = 35°, AB = 5cm, AC = 7 cm and
BC = 3 cm. Find CD.
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Answer 1

Answer:

Answer is - 4.2 cm

Step-by-step explanation:

By angle bisector theorm,

       AB/AC = BD/CD

         5/7 =  3/X

           X =  7*3/5

              =  21/5

             X= 4.2 cm

Answer 2

Given:

• ∠EAB = 110°
• ∠CAD = 35°
• Length AB = 5cm
• Length AC = 7cm
• Length BC = 3cm

To Find:

Length CD

Explanation:

∠EAB + ∠CAD + ∠BAD = 180°          

All the three angles lie on a straight line and on a point hence they add up to 180°

Hence ,

110° + 35° + ∠BAD = 180°         (Given)

145° + ∠BAD = 180°

∠BAD = 180° - 145°

Therefore       ∠BAD = 35°

Hence, ∠BAD = ∠CAD = 35°

This proves that line segment AD is the Angle Bisector of ∠BAC

Hence, point D divides the line segment BC into two Equal Halves

Due to Angle Bisector Theorem.

Length BC = 3cm

Length BC = Length BD + Length CD

Since point D divides the line segment BC into two Equal Halves.

Length BD = Length CD

Length BC  = Length BD + Length BD

Length BC = 2 x Length BD

$\frac{Length BC}{2}$ = Length BD

$\frac{3}{2}$cm = Length BD

∴Length BD = 1.5 cm

Since Length BD = Length CD

Therefore, Length CD = 1.5cm