Base BC of an equilateral triangle ABC is root2 x+y+2=0. If vertex A is the origin, then the area of triangle ABC is (in sq. units)
A) 3 root3
B) 2/3 root3
C) 4/3 root3
D) 6 root3
Answers
Answer:
A) 3 root3
B) 2/3 root3
C) 4/3 root3
D) A) 3 root3
B) 2/3 root3
C) 4/3 root3
D) 6 root3 A) 3 root3
B) 2/3 root3
C) 4/3 root3
D) 6 root3 A) 3 root3
B) 2/3 root3
C) 4/3 root3
D) 6 root3 6 root3
Step-by-step explanation:
A) 3 root3
B) 2/3 root3
C) 4/3 root3
A) 3 root3
B) 2/3 root3
C) 4/3 root3
D) 6 root3 D) 6 root3
Given : Base BC of an equilateral triangle ABC is √2 x+y+2=0
vertex A is the origin,
To Find : area of triangle ABC is (in sq. units)
Solution:
Distance of vertex A ( 0 , 0) from √2 x+y+2=0 will give height of the triangle
h = | ( √2 (0)+0 +2 ) /( √ ((√2)² + 1² )) |
=> h = 2/√3
h = √3 x/ 2 where x is side of Equilateral triangle
Hence 2/√3 = √3 x/ 2
=> x = 4/3
Area of Triangle = (1/2) * base * height
= (1/2) * (4/3) * (2/√3)
= 4/3√3 sq units
Area of Triangle = 4/3√3 sq units
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