SOLUTION: A right angled triangle has sides (3x+1)cm being the longest side (x+2)cm and (x-1)cm being the other side.Find x

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Question 1093142: A right angled triangle has sides (3x+1)cm being the longest side (x+2)cm and (x-1)cm being the other side.Find x
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the hypotenuse is the longest side of a right triangle.

the other 2 sides are legs of the right triangle.

pythagorus theorem states that a^2 + b^2 = c^2

a and b are legs.
c is the hypotenuse.

your formula becomes (x+2)^2 + (x-1)^2 = (3x+1)^2

(x+2) is one leg.
(x-1 is the other leg.
(3x+1) is the hypotenuse.

(x+2)^2 is equal to (x+2) * (x+2) which is equal to x^2 + 2x + 2x + 4 which is equal to x^2 + 4x + 4

(x-1)^2 is equal to (x-1) * (x-1) which is equal to x^2 - x - x + 1 which is equal to x^2 - 2x + 1

(3x+1)^2 is equal to (3x+1) * (3x+1) whiich is equal to 9x^2 + 3x + 3x + 1 which is equal to 9x^2 + 6x + 1.

(x+2)^2 + (x-1)^2 = (3x+1)^2 becomes:

(x^2 + 4x + 4) + (x^2 - 2x + 1) = (9x^2 + 6x + 1)

subtract (9x^2 + 6x + 1 from both sides of the equation to get:

(x^2 + 4x + 4) + (x^2 - 2x + 1) - (9x^2 + 6x + 1) = 0

simplify by removing parentheses to get:

x^2 + 4x + 4 + x^2 - 2x + 1 - 9x^2 - 6x - 1 = 0

reorder the terms so that like terms are together to get:

(x^2 + x^2 - 9x^2) + (4x - 2x - 6x) + (4 + 1 - 1) = 0

combine like terms to get:

(-7x^2) + (-4x) + (4) = 0

remove parentheses to get:

-7x^2 - 4x + 4 = 0

solutions to this equation are:

x = -1.0938363213561 or x = 0.52240774992748

with the use of these values of x, you will find that:

(x+2)^2 + (x-1)^2 = (3x+1)^2

if your round your answers to 3 decimal digits, then you will ge4t:

x = -1.094 or x = .522

you can graph these equations to solve them in a couple of basic ways.

the first way is to graph the equations of:

y = (x+2)^2 + (x-1)^2 and y = (3x+1)^2.

the intersection of these two equations will be your solution.

the second way is to graph the equation of:

y = (x+2)^2 + (x-1)^2 - (3x+1)^2.

your solution will be when the graph crosses the x-axis.

this can be done because:

if a + b = c, then a + b - c = 0

that last form of the equations happens when you subtract c from both sides of the equation.

here's the graph of the first way.

the red graph is the equation of y = (x+2)^2 + (x-1)^2
the blue graph is the equation of y = (3x+1)^2

the intersection of those two equations shows the solution.

when x = -1.094, y = 5.205
when x = .522, y = 6.591

here's the graph of the second way.

the red graph shows the following solutions.

when x = -1.094, y = 0
when x = .522, y = 0

both ways lead to the solution that x = -1.094 or x = .522.

you will reject x = -1.094 because the dimensions of a triangle can't be negative.

therefore, the only solution is that x = .522 rounded to 3 decimal digits.