Question 620095: The sides of an equilateral triangle are given as x+3y,3x+2y-2 and 4x+1/2y+1 respectively.Find the lengths of the sides Answer by math-vortex(648) (Show Source):
You can put this solution on YOUR website! Hi, there--
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To solve this problem, we will use the definition of an equilateral triangle. By definition, all three sides are equal in length. Using this fact, we can generate several equations. (NOTE: I assumed that the third side of the triangle has 1/2 as a coefficient of the y-term. It was difficult to tell what you meant; please make sure that I am solving the problem using the correct values. If not, email me and I'll make corrections.)
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Now we can use any two of the equations above to solve the problem. In essence, we want a value of x and y which are true for both equations. Let's use the first two equations. (It doesn't matter which two you choose.)
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Step I: Simplify the first equation into slope-intercept form (y=...). Subtract x from both sides.
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Subtract 2y from both sides.
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Step 2: Use the substitution Method to solve the system of equation. Substitute 2x-2 for y in the second equation.
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Simplify by combining like terms.
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Substitute 3 for x in the first equation.
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Simplify by combining like terms.
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STEP III: Check your work.
We have x=3 and y=4 as a solution to the system of equations. Since we have an equilateral triangle, these values should yield sides of equal length.
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x+3y --> (3)+3(4)=3+12=15
3x+2y-2 --> 3(3)+2(4)-2=9+8-2=15
4x+(1/2)y+1 --> 4(3)+(1/2)(4)+1=12+2+1=15
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Check, check, check! The three sides of the triangle each have length of 15 units.
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Hope this helps. Feel free to email me if you have questions about this.
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Ms.Figgy
math.in.the.vortex@gmail.com
