Question

Label the vertices and state the Pythagorean Theorem for the following right triangle. Find x.

Answer 1

Answer: 9

Explanation:

Follow this

Answer 2

Pythagorean Theorem Statement is below.

Therefore the value of x is 9 m.

Explanation:

Given:

Label the vertices as A , B , C shown in figure below such that

∠A = 90°

AC = Longer leg = 12 m

AB = Shorter leg = x

BC = Hypotenuse = 15 m

To Find:

x = ?

Solution:

Pythagorean Theorem :

Pythagorean Theorem States that "the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides".

Which can be Written as

`(\textrm{Hypotenuse})^(2) = (\textrm{One Side})^(2)+(\textrm{Other Side})^(2)`

OR

`(\textrm{Hypotenuse})^(2) = (\textrm{Shorter leg})^(2)+(\textrm{Longer leg})^(2)`

i.e
`(BC)^(2)=(AB)^(2)+(AC)^(2)`

Substituting the values AB ,AC, BC we get

`(15)^(2)=(x)^(2)+(12)^(2)\\(x)^(2)=225-144=81\\(x)^(2)=81\\Square\ Rooting\\x=√(81)=9\\x=9\ m`

Therefore the value of x is 9 m.