Question

Find the lettered side e cm​

Answer 1

`√(122)\approx{11.05}`

Explanation:

In any right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse. This is commonly represented by the equation
`a^2+b^2=c^2`.

In the triangle on the left:

`a^2+b^2=c^2`

`5^2+9^2=c^2`

`25+81=c^2`

`106=c^2`

`√(106)=c`

The hypotenuse of the triangle on the left becomes a leg of the triangle on the right, so we repeat the process:

`a^2+b^2=c^2`

`4^2+(√(106))^2=c^2`

`16+106=c^2`

`122=c^2`

`√(122)=c`

`c\approx{11.05}`