Question

An equilateral triangle and a right-angled triangle, having the same base are inscribed within the same circle. What is the ratio of area of the equilateral triangle to area of the right-angled triangle?​

Answer 1

Answer:

3 : 2

Step-by-step explanation:

$A_{equ}$ = (√3 × x²) / 4

$A_{right}$ = (√3 × x²) / 6

$A_{equ}$ : $A_{right}$ = 6 : 4 = 3 : 2

Answer 2

Given : An equilateral triangle and a right-angled triangle, having the same base are inscribed within the same circle.  

To find : ratio of area of the equilateral triangle to area of the right-angled triangle

Solution:

ABC    equilateral triangle   & ABD  - right angle triangle

Let say Base of triangle  AB  =   a  unit

the area of ΔABC = (√3 / 4)a²

ABC is equilateral triangle => ∠ACB = 60°

Both triangle area inscribed in same circle & base is common

hence ∠ADB = ∠ACB  ( angle by same Chord AB)

=>  ∠ADB = 60°

Tan ∠ADB  =  AB/BD

=> Tan 60°  = a /BD

=> BD = a/√3

Area of right angle triangle = (1/2) AB * BD

= (1/2) a * a/√3

= (√3 /6 )a²

ratio of area of the equilateral triangle to area of the right-angled triangle

=  (√3 / 4)a²  / (√3 /6 )a²  

= 6/4

= 3/2

ratio of area of the equilateral triangle to area of the right-angled triangle = 3 : 2

Learn more:

In triangle ABC B=90 BD is perpendicular to AC The ratio of area ...

https://brainly.in/question/15107670

Let abcdef be a regular hexagon.What is the ratio of area of triangle ...

https://brainly.in/question/9345584