Home
Class 11
MATHS
The equation of the base of an equilater...

The equation of the base of an equilateral triangle is `x+y=2` and its vertex is `(2,-1)dot` Find the length and equations of its sides.

Text Solution

Verified by Experts

The correct Answer is:
N/a
Given that, equilateral `DeltaABC` having equation of base is `x+y=2`.
In `DeltaABD, sin60^@=(AD)/(AB)`
`rArr AD=AB sin 60^@=ABsqrt3/(2)`
`because AD =ABsqrt3/(2)`......(i)
Now the length of perpendicular from `(2,-1)` to the line `x+y=2` is given by `AD=|(2+(-1)-2)/(sqrt(1^2+1^2))|=(1)/sqrt(2)`
From Eq.(i) , `(1)/(sqrt2)=AB(sqrt3)/(2)AB=sqrt(2/3)`
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    NCERT EXEMPLAR ENGLISH|Exercise Objective type questions|20 Videos

  • STRAIGHT LINES

    NCERT EXEMPLAR ENGLISH|Exercise Fillers|6 Videos

  • STRAIGHT LINES

    NCERT EXEMPLAR ENGLISH|Exercise MATCHING THE COLUMN|3 Videos

  • STATISTICS

    NCERT EXEMPLAR ENGLISH|Exercise FILLERS|7 Videos

  • TRIGONOMETRIC FUNCTIONS

    NCERT EXEMPLAR ENGLISH|Exercise TRUE/FALSE|9 Videos

Similar Questions

Explore conceptually related problems

Equation of the base of an equilateral triangle is 3x + 4y = 9 and its vertex is at point (1,2) .Find the equations of the other sides and the length of each side of the triangle .

If the equation of base of an equilateral triangle is 2x-y=1 and the vertex is (-1,2), then the length of the sides of the triangle is sqrt((20)/3) (b) 2/(sqrt(15)) sqrt(8/(15)) (d) sqrt((15)/2)

The equation of the base of an equilateral triangle is x+y-2=0 and the opposite vertex has coordinates (2, -1). Find the area of the triangle.

If the equation of base of an equilateral triangle is 2x-y=1 and the vertex is (-1,2), then the length of the sides of the triangle is (a) sqrt((20)/3) (b) 2/(sqrt(15)) (c) sqrt(8/(15)) (d) sqrt((15)/2)

The side of an equilateral triangle is 3.5 cm. Find its perimeter

If the centroid of an equilateral triangle is (2, -2) and its one vertex is (-1, 1) , then the equation of its circumcircle is

A vertex of an equilateral triangle is (2,3) and the opposite side is x+y=2. Find the equations of other sides.

If the centroid of an equilateral triangle is (1,1) and its one vertex is (2,-1) , then equation of the circumcircle of the triangle is

A vertex of an equilateral triangle is 2,3 and the opposite side is x+y=2. Find the equations of other sides.

The equation of one side of an equilateral triangle is x-y=0\ and one vertex is (2+sqrt(3),\ 5) . Prove that a second side is y+(2-sqrt(3))x=6 and find the equation of the third side.