Given: △ABC m∠B=90°, AB:BC=4:5 BD ⊥ AC , BD=80 Find: AD and DC

Question

Given: △ABC

       m∠B=90°, AB:BC=4:5

       

BD

 ⊥ 

AC

 , BD=80

    Find: AD and DC

 

Answer 1

triangle DAC is similar to triangle DBC

corresponding parts of similar triangles form equal ratios

separate the triangles and orient them the same way

AD corresponds to BD

DB corresponds to DC

AB corresponds to BC

AB/BC=4/5=DB/DC

4/5=DB/DC

4/5=80/DC

multiply both terms by 20

DC=100 (one answer)

DB/DC=AD/BD

80/100=AD/80

cross multiply

100AD=80*80

100AD=6400

AD=64 (second answer)

check:

using triangle ADB and the Pythagorean Theorem

64^2+80^2=AB^2

10,496=AB^2

AB=102.44999

using triangle BDC and the Pythagorean Theorem

80^2+100^2=BC^2

16,400=BC^2

BC=128.06248

now use triangle BAC

AB^2+BC^2=AC^2

10,496+16,400=164^2

26,896=26,896