Height of the cuboid

Cuboid with a rectangular base, measuring 3 cm and 4 cm diagonal has a body 13 centimeters long. What is the height of the cuboid?

Result

c =  12 cm

Solution:

a=3 cm b=4 cm u=13 cm  s2=a2+b2 s=a2+b2=32+42=5 cm  u2=c2+s2  c=u2−s2=132−52=12 cma=3 \ \text{cm} \ \\ b=4 \ \text{cm} \ \\ u=13 \ \text{cm} \ \\ \ \\ s^2=a^2 + b^2 \ \\ s=\sqrt{ a^2+b^2 }=\sqrt{ 3^2+4^2 }=5 \ \text{cm} \ \\ \ \\ u^2=c^2 + s^2 \ \\ \ \\ c=\sqrt{ u^2-s^2 }=\sqrt{ 13^2-5^2 }=12 \ \text{cm}

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Pythagorean theorem is the base for the right triangle calculator.
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