The length of the side BC is [tex]\boxed{15{\text{ units}}}.[/tex]
Further explanation:
The Pythagorean formula can be expressed as,
[tex]\boxed{{H^2} = {P^2} + {B^2}}.[/tex]
Here, H represents the hypotenuse, P represents the perpendicular and B represents the base.
Given:
The length of the side AB is [tex]9{\text{ units}}.[/tex]
The length of the side AC is [tex]12{\text{ units}}.[/tex]
The options are as follows,
(A). 21
(B). 15
(C). 225
(D). 63
(E). 3
(F). [tex]\sqrt {63}[/tex]
Explanation:
The hypotenuse of the triangle ABC is BC.
The perpendicular of the triangle ABC is AB.
The base of the triangle ABC is AC.
Use the Pythagoras formula in triangle ABC to obtain the length of side BC.
[tex]\begin{aligned}{\left( {BC} \right)^2}&={\left( {AC} \right)^2} + {\left( {AB} \right)^2}\\{\left( {BC} \right)^2}&={\left( {12} \right)^2} + {\left( 9 \right)^2}\\{\left( {BC} \right)^2} &= 144 + 81\\{\left( {BC} \right)^2}&= 225\\\end{aligned}[/tex]
Further solve the above equation.
[tex]\begin{aligned}{\left( {BC}\right)^2} &= 225\\BC &= \sqrt {225}\\BC &= 15\\\end{aligned}[/tex]
Hence, the length of the side BC is [tex]\boxed{15{\text{ units}}}.[/tex]
Option (A) is not correct.
Option (B) is correct.
Option (C) is not correct.
Option (D) is not correct.
Option (E) is not correct.
Option (F) is not correct.
Learn more:
1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Trigonometry
Keywords: perpendicular bisectors, sides, right angle triangle, triangle, altitudes, hypotenuse, on the triangle, hypotenuse, trigonometric functions, Pythagoras theorem, formula.
