. Triangle ABC is an equilateral triangle with each side of length 2p. If AD parellaer BC then the value of AD is
Answers
Given : Triangle ABC is an equilateral triangle with each side of length 2p. AD ⊥ BC
( correction in Question AD parallel BC should be AD perpendicular BC)
To Find : value of AD is
Solution:
ABC is an equilateral triangle hence all side lengths are equal
AB = BC = AC = 2p
AD ⊥ BC
in ΔADB and ΔADC
AD = AD common
AB = AC ( Equal sides of equilateral triangle)
∠ADB = ∠ADC = 90° given
=> ΔADB ≅ ΔADC ( using RHS Congruency)
RHS - Right angle Hypotenuse congruence
Corresponding parts of congruence triangles are congruent
Hence BD = CD
BD + CD = 2p
=> BD = CD = p
in Δ ABD
Using Pythagorean theorem:
square on the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two perpendicular sides.
=> AB² = AD² + BD²
=> (2p)² = AD² + p²
=> 4p² = AD² + p²
=> AD² = 3p²
=> AD = √3 p
Value of AD is √3 p
Learn More:
In triangle ABC B=90 BD is perpendicular to AC The ratio of area ...
brainly.in/question/15107670
Let abcdef be a regular hexagon.What is the ratio of area of triangle ...
brainly.in/question/9345584