Question

In the given figure, if AB = 3 cm and AC = 5 cm, then CD is equal to
(a) 4 cm
(b) 2 cm
(c) 3 cm
(d) 5 cm​

Answer 1

Answer:

AB^2 + BC^2 = AC^2

9 + BC^2 = 25

BC = 4 cm

CD = 4 cm ( BC = CD )

Hence, correct option is (a) 4 cm

Answer 2

Given  : AB = 3 cm and AC = 5 cm

AC is bisector of angle BAD

To Find : CD

(a) 4 cm

(b) 2 cm

(c) 3 cm

(d) 5 cm​

Solution:

ΔABC is right angle

Pythagoras  theorem:  

Square on the hypotenuse of a right-angled triangle is equal to the  

sum of the squares of the other two perpendicular sides.

AC² = AB² + BC²

=> 5² = 3² + BC²

=> BC² = 4²

=> BC = 4 cm

in Δ ABC and ΔADC

∠BAC = ∠DAC  as  AC is bisector of angle BAD

∠ABC = ∠ADC = 90°

AC = AC   common

=> ΔABC ≅ ΔADC  using AAS congruence

Hence

BC = CD   using corresponding parts of congruent triangles are equal

Hence , CD = 4 cm

Correct option is  a) 4 cm

Learn More:

Solve a proportion to find the missing side. The figures are similar to ...

brainly.in/question/17153989

we know in a triangle sum of any two sides is greater than the third ...

brainly.in/question/6691141