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If the equation of the base of an equilateral triangle is x + y = 2 and the vertex is (2, –1), then find the length of the side of the triangle.

(Hint: Find the length of the perpendicular (p) from (2, –1) to the line and use p = l sin 60°, where l is the length of the side of the triangle.)

0 3 Views | Posted 4 months ago
Asked by Shiksha User

  • 1 Answer

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    Answered by

    Vishal Baghel | Contributor-Level 10

    4 months ago

    This is a Long Answer Type Questions as classified in NCERT Exemplar

    Sol:

    Equation  of  the  base  AB  of  a  ΔABC  is  x+y=2In  ΔABD,               sin600=ADAB      ⇒32=ADAB    ⇒AD=32ABLength  of  perpendicular  from  A(2,−1)  to  the  line  x+y=2  is             AD=|1×2+1×−1−2(1)2+(1)2|⇒32AB=|2−1−22|=|−12|⇒32AB=12        ⇒AB=23Hence,  the  required  length  of  side=23.

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