Q8. The sides of an equilateral triangle are shortened by 12 units, 13 units and 14 units respectively and a right angle triangle is formed. Find the length of each side of the equilateral triangle.
Answers
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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