Question

Calculate the measure of the hypotenuse of a right triangle, whose legs measure 5 and 12 cm​

Answer 1

13 cm

Explanation:

Pythagoras Theorem explains the relationship between the three sides of a right triangle. The square of the hypotenuse (longest side) is equal to the sum of the squares of the legs of a right triangle:

`\large\boxed{a^2+b^2=c^2}`

Where:

• a and b are the legs of the right triangle.
• c is the hypotenuse (longest side) of the right triangle.

Given:

• a = 5 cm
• b = 12 cm

Substitute the given values into the formula and solve for c:

`\begin{aligned} a^2+b^2&=c^2\\\implies5^2+12^2&=c^2\\25+144&=c^2\\169&=c^2\\c^2&=169\\√(c^2)&=√(169)\\c&=13\end{aligned}`

Therefore, the measure of the hypotenuse is 13 cm.