A right-angled triangled has sides (x+10)cm,(x+2)cm and (x+4). find the value of each side of the triangle.
To find the value of each side of the right-angled triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we have the sides (x+10)cm, (x+2)cm, and (x+4)cm. We need to determine the value of x.
According to the Pythagorean theorem, we can write the equation as follows:
(x+10)^2 = (x+2)^2 + (x+4)^2
Expanding both sides of the equation:
x^2 + 20x + 100 = x^2 + 4x + 4 + x^2 + 8x + 16
Combine like terms:
x^2 + 20x + 100 = 3x^2 + 12x + 20
Rearrange the equation:
0 = 2x^2 - 8x - 80
Simplify the equation:
0 = x^2 - 4x - 40
Since this is a quadratic equation, we can factor it or use the quadratic formula. In this case, let's factor the equation:
0 = (x - 10)(x + 4)
Setting each factor equal to zero:
x - 10 = 0 or x + 4 = 0
Solving for x:
x = 10 or x = -4
Since we are dealing with side lengths, we can discard the negative value and choose x = 10.
Now, we can substitute x = 10 into the given expressions for the sides to find their respective values:
1. For the first side (x+10)cm:
(x+10)cm = (10+10)cm = 20cm
2. For the second side (x+2)cm:
(x+2)cm = (10+2)cm = 12cm
3. For the third side (x+4)cm:
(x+4)cm = (10+4)cm = 14cm
Therefore, the value of each side of the triangle is 20cm, 12cm, and 14cm respectively.
Well, well, well, we have ourselves a right-angled triangle here, huh? Let's dive into it and solve the mystery of the sides!
So we're given that one side is (x + 10) cm, another side is (x + 2) cm, and the hypotenuse is (x + 4) cm.
Now, in a right-angled triangle, we have a lovely thing called the Pythagorean theorem. It states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. Fancy, right?
So we can set up our equation like this:
(x + 10)^2 + (x + 2)^2 = (x + 4)^2
Now, let's solve this quadratic equation! Expand those squares, combine like terms, and let the math magic happen:
x^2 + 20x + 100 + x^2 + 4x + 4 = x^2 + 8x + 16
Simplifying further, we get:
2x^2 + 24x + 108 = x^2 + 8x + 16
Subtracting x^2 and 8x from both sides, we get:
x^2 + 16x + 92 = 0
And now, my comedic genius, it's time to whip out the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
Plugging in the values for a, b, and c, we get:
x = (-16 ± √(16^2 - 4*1*92))/(2*1)
After a little bit more number crunching, we find that x = -6 or x = -10.
But hold your laughter, my friend! We can't have negative side lengths in our surreal triangle, now can we? So let's throw out those negative solutions and focus on the positive ones.
When x = -6, the sides of our triangle are 4 cm, -4 cm, and -2 cm. Uh-oh, that's not possible!
But when x = -10, the sides of our triangle are 0 cm, -8 cm, and -6 cm. Yikes, that's even worse!
So, my friend, it seems like there's no real solution that satisfies the conditions. The sides of the triangle remain a mystery, unsolved, and probably haunting the dreams of mathematicians everywhere.
But hey, at least we had fun along the way, right? Keep smiling and keep searching for those right-angled triangles!
A right angled
Opor gan
Mathe
solve:
(x+2)^2 + (x+4)^2 = (x+10)^2
hint: x will be irrational, that's ok, it checks out