Question

Please Help! Given the right triangles ABC and ABD, what is the length of segment BC, in units?

Answer 1

Answer:

20 units

Step-by-step explanation:

Consider right triangle ABD. In this triangle,

$BD=37\ un.\\ \\AD=19+16=35\ un.$

By the Pythagorean theorem,

$BD^2=AD^2+AB^2\\ \\37^2=35^2+AB^2\\ \\AB^2=37^2-35^2=(37-35)(37+35)=2\cdot 72=144\\ \\AB=12\ un.$

Consider right triangle ABC. In this triangle,

$AC=16\ un.\\ \\AB=12\ un.$

By the Pythagorean theorem,

$BC^2=AB^2+AC^2\\ \\BC^2=16^2+12^2\\ \\BC^2=256+144=400\\ \\BC=20\ un.$