In triangle A B C, D is a point on A C such that B D perp A C. If angle A B C=90°, A B=20 mathrm~cm, and B D=12 mathrm~cm, then find the length of B C (in mathrmcm ).

Question

In triangle A B C, D is a point on A C such that B D perp A C. If angle A B C=90°, A B=20 mathrm~cm, and B D=12 mathrm~cm, then find the length of B C (in mathrmcm ). (A) 12 (B) 15 (C) 16 (D) 25

Tardigrade Admin · Accepted Answer

text In triangle A B D, A D2=A B2-B D2 =A D2=202-122=400-144=256=162 ⇒ A D=16 mathrm~cm text We have B D2=A D ⋅ C D ⇒ 122=16 ⋅ C D ⇒ C D=9 mathrm~cm text In triangle B D C, B C2=B D2+C D2=122+92 =144+81=225=152 ⇒ B C=15 mathrm~cm

Q. In △ABC,D is a point on AC such that BD⊥AC. If ∠ABC=90∘,AB=20 cm, and BD=12 cm, then find the length of BC (in cm ).

12

15

16

25

In △ABD,AD2=AB2−BD2 =AD2=202−122=400−144=256=162 ⇒AD=16 cm We have BD2=AD⋅CD ⇒122=16⋅CD⇒CD=9 cm In △BDC, BC2=BD2+CD2=122+92 =144+81=225=152 ⇒BC=15 cm

Q. In $△ A BC, D$ is a point on $A C$ such that $B D ⊥ A C$ . If $∠ A BC = 9 0^{\circ}, A B = 20 cm$ , and $B D = 12 cm$ , then find the length of $BC$ (in $cm$ ).