Question

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

Answer 1

Answer:

Pythagorean Theorem Statement is below.

Therefore the value of x is 9 m.

Step-by-step 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

$(15)^{2}=(x)^{2}+(12)^{2}\\(x)^{2}=225-144=81\\(x)^{2}=81\\Square\ Rooting\\x=\sqrt{81}=9\\x=9\ m$

Therefore the value of x is 9 m.