In a triangle, the two sides are 10 cm and 8 cm.This triangle will be rectangular if the third side is equal to how many?

In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the legs c ^ 2 = a ^ 2 + b ^ 2. The hypotenuse is the longest side of a right-angled triangle, therefore 2 options are possible:

1) Sides 10 cm and 8 cm – legs. Then, according to the Pythagorean formula:

c ^ 2 = 10 ^ 2 + 8 ^ 2 = 100 + 64 = 164;

c = √164 = √ (4 * 41) = 2√41.

2) Side 10 cm – hypotenuse, side 8 cm – leg.

10 ^ 2 = a ^ 2 + 8 ^ 2;

100 = a ^ 2 – 64;

a ^ 2 = 100 – 64 = 36;

a = √36 = 6.

Answer: a triangle with sides 10 cm and 8 cm will be rectangular if the third side is 6 or 2√41.