The length of one leg of the triangle [tex]\boxed{5\sqrt {10} }.[/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.
Isosceles triangle has 2 sides equal to each other and the two base angles are equal to each other.
Given:
The length of the hypotenuse is [tex]10\sqrt 5.[/tex]
The options are as follows,
(A). [tex]5\sqrt 5[/tex]
(B). [tex]5\sqrt {10}[/tex]
(C). [tex]10\sqrt {5}[/tex]
(D). [tex]10\sqrt {10}[/tex]
Explanation:
The length of the hypotenuse is [tex]10\sqrt 5.[/tex]
Consider the length of other leg of the triangle [tex]x[/tex].
Use the Pythagoras formula in triangle ABC.
[tex]\begin{aligned}{\left( {10\sqrt 5 }\right)^2}&= {\left( x \right)^2} + {\left( x \right)^2}\\100 \times 5&= 2{x^2}\\\frac{{500}}{2}&= {x^2}\\250&= {x^2}\\\end{aligned}[/tex]
Further solve the above equation.
[tex]\begin{aligned}{x^2}&= 250\\x&= \sqrt {250}\\x&= 5\sqrt {10} \\\end{aligned}[/tex]
Hence, the length of one leg of the triangle [tex]\boxed{5\sqrt {10} }.[/tex]
Option (A) is not correct.
Option (B) is correct.
Option (C) is not correct.
Option (D) 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: length of the leg, triangle, isosceles,perpendicular bisectors, sides, right angle triangle, triangle, altitudes, hypotenuse, on the triangle, hypotenuse, trigonometric functions, Pythagoras theorem, formula.
