Mathematics: Given the right triangles abc and abd, what is the length of segment bc, in units?

Given the right triangles abc and abd, what is

zaida00

14.01.2022

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,

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

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cicilee49

07.04.2020

Step-by-step explanation:

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