Given a rectangle ABCD. EA is perpendicular to plane ABCD. Find the length EC if AB = 4cm, AD = 3cm, AE = 12cm.

AB = 4 cm and AD = 3 cm – these are the sides of the rectangle ABCD and the legs of the right triangle ABC.

The diagonal AC of the rectangle is also the hypotenuse of the triangle ABC.

By the Pythagorean theorem, we find the hypotenuse.

4 ^ 2 + 3 ^ 2 = 25.

The root of 25 is 5.

Now consider the EAC triangle. EA is perpendicular to the ABCD plane. From here we see that EA is the leg of the right-angled triangle EAC. AC is also a leg of the EAC triangle.

Let’s find the hypotenuse EC.

12 ^ 2 + 5 ^ 2 = 144 + 25 = 169.

The root of 169 is 13.

Answer: EU = 13 cm.

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