# The legs of a right-angled triangle are 30 and 40. Find the hypotenuse of this triangle.

December 29, 2020 | education

| Given: right-angled triangle ABC;

angle C = 90;

leg AC = 30 centimeters;

leg CB = 40 centimeters.

Find: hypotenuse AB -?

Decision:

Consider a right-angled triangle ABC. By the Pythagorean theorem (the square of the hypotenuse is equal to the sum of the squares of the legs):

AC ^ 2 + BC ^ 2 = AB ^ 2

AB ^ 2 = 30 ^ 2 + 40 ^ 2;

AB ^ 2 = 30 * 30 + 40 * 40;

AB ^ 2 = 900 + 1600;

AB ^ 2 = 2500;

AB = √ 2500

AB = 50 centimeters – the length of the hypotenuse.

Answer: 50 centimeters.

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