Asked by Temitope
The perimeter of an isosceles triangle is 28cm. AB =4ycm,AC=(6y-2x+1)cm and BC =(x+2y)cm. Find x and y, state the lengths of the triangle.
Answers
Answered by
Steve
You know that the perimeter is 28, meaning
4y + 6y-2x+1 + x+2y = 28
x-12y = -27
Since the triangle is isosceles, you also need one of these equations:
4y = 6y-2x+1
4y = x+2y
6y-2x+1 = x+2y
So, just work your way through the possibilities, and you wind up with
(x,y) = (3,5/2)
(x,y) = (27/5,27/10)
(x,y) = (15/4,41/16)
Now, just check those solutions to see which one(s) produce values that qualify for sides of a triangle: No negative lengths, each side less than the sum of the other two.
4y + 6y-2x+1 + x+2y = 28
x-12y = -27
Since the triangle is isosceles, you also need one of these equations:
4y = 6y-2x+1
4y = x+2y
6y-2x+1 = x+2y
So, just work your way through the possibilities, and you wind up with
(x,y) = (3,5/2)
(x,y) = (27/5,27/10)
(x,y) = (15/4,41/16)
Now, just check those solutions to see which one(s) produce values that qualify for sides of a triangle: No negative lengths, each side less than the sum of the other two.
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