SOLUTION: The sides of an equilateral triangle are shortened by 12 units,13 units and 14 units respectively and a right angled triangle is formed.Find the side of the equilateral triangle.

Question 255064: The sides of an equilateral triangle are shortened by 12 units,13 units and 14 units respectively and a right angled triangle is formed.Find the side of the equilateral triangle.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x = 17.

17 - 14 = 3
17 - 13 = 4
17 - 12 = 5

345 triangle is a right triangle.

solve by use of pythatogrean formula.

a^2 + b^2 = c^2

x is the side of the equilateral triangle.

(x-12) = largest side which would be equal to c.

(x-13) = midsize side which would be equal to b.

(x-14) = smallest side which would be equal to a.

a^2 + b^2 = c^2 becomes:

(x-14)^2 + (x-13)^2 = (x-12)^2

this becomes

x^2 - 28x + 196 + x^2 - 26x + 169 = x^2 - 24x + 144

combine like terms to get:

2x^2 - 54x + 365 = x^2 - 24x + 144

subtract x^2 from both sides of equation to get:

x^2 - 54x + 365 = -24x + 144

add 24x to both sides of equation to get:

x^2 - 30x + 365 = 144

subtract 144 from both sides of equation to get:

x^2 - 30x + 221 = 0

factor this quadratic equation to get:

(x-17) * (x-13) = 0

this makes x = 17 or x = 13.

x can't be 13 because then one of the sides of the triangle will be 0.

x has to be 17.

when x is 17, you get:

x-12 = 17-12 = 5
x-13 = 17-13 = 4
x-14 = 17-14 = 3

that's your 345 triangle which is a right triangle.

side of the equilateral triangle is 17.

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