Question

Find each of the missing sides of the right triangles using Pythagorean Theorem1.2.

Answer 1

The Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of squares of the other 2 legs in a triangle.

`\begin{gathered} c^2=a^2+b^2 \\ \text{where} \\ c\text{ is the hypotenuse} \\ a\text{ and }b\text{ are the other two legs of a right triangle} \end{gathered}`

In the given figure, we have side lengths 3 and 4, with the value of the hypotenuse missing.

Substitute the following values to get the missing length of the hypotenuse

`\begin{gathered} c=x \\ a=3 \\ b=4 \\ c^2=a^2+b^2 \\ (x)^2=(3)^2+(4)^2 \\ x^2=9+16 \\ x^2=25 \end{gathered}`

Get the square root of both sides to get the value of the hypotenuse

`\begin{gathered} \sqrt[]{x^2}=\sqrt[]{25} \\ x=5 \end{gathered}`

Therefore, the missing side length x is equal to 5 units.