“The sides of an equilateral triangle are given as 5x cm,(4x+3y-9)cm and(6x-2y+2)cm.Find the value of x and y and hence calculate the perimeter of the triangle”
Answers
Answer:
Side of equilateral Triangle = 60 cm
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Step-by-step explanation:
Given:
sides of given equilateral triangle
5x cm
(4x + 3y - 9) cm
(6x - 2y + 2) cm
To find:
values of x and y and perimeter of the triangle.
Answer:
Sides are equal in an equilateral triangle.
Therefore,
=> 5x = 4x + 3y - 9
=> x - 3y + 9 = 0 -------- (1)
Also we have,
=> 5x = 6x - 2y + 2
=> x - 2y + 2 = 0 ---------(2)
And,
=> 4x + 3y - 9 = 6x - 2y + 2
=> 2x - 5y + 11 = 0 --------(3)
From eq (1) and (2)
we will get,
=> y - 7 = 0
=> y = 7
Substituting this value in eq (1)
=> x - (2)(7) + 2 = 0
=> x - 14 + 2 = 0
=> x - 12 = 0
=> x = 12
It's given that, side of equilateral triangle is 5x.
Therefore,
Side = 5 × 12 = 60 cm
We know that perimeter of equilateral triangle = 3(side)
Thus,
Perimeter = (3 × 60) = 180 cm