In the triangle A B C, angle A B C or angle B=90° . A B: B D: D C=3: 1: 3. If A C=20 cm, then what is the length of A D (in cm ) ?

Question

In the triangle A B C, angle A B C or angle B=90° . A B: B D: D C=3: 1: 3. If A C=20 cm, then what is the length of A D (in cm ) ? (A) 5 √2 (B) 6 √3 (C) 4 √5 (D) 4 √10

Tardigrade Admin · Accepted Answer

(i) Apply 'Pythagoras theorem' for triangle A B C. (ii) Let A B=3 x, B D=x and C D=3 x. (iii) First find A B and B C using A B2+B C2=A C2. (iv) Then find A D by using A D2=A B2+B D2.

Q. In the triangle $A BC, ∠ A BC$ or $∠ B = 9 0^{\circ} . A B : B D$ : $D C = 3 : 1 : 3$ . If $A C = 20 c m$ , then what is the length of $A D$ (in $c m)$ ?

$52$

$63$

$45$

$410$

(i) Apply 'Pythagoras theorem' for triangle $A BC$ .
(ii) Let $A B = 3 x, B D = x$ and $C D = 3 x$ .
(iii) First find $A B$ and $BC$ using $A B^{2} + B C^{2} = A C^{2}$ .
(iv) Then find $A D$ by using $A D^{2} = A B^{2} + B D^{2}$ .

Q. In the triangle ABC,∠ABC or ∠B=90∘.AB:BD : DC=3:1:3. If AC=20cm, then what is the length of AD (in cm) ?

52​

63​

45​

410​