The hypotenuse of a triangle is 10cm long. The two shorter sides are xcm and x+2 cm. Find the valtue of x?
Side^2+side^2
10^2={x+2)^2+x^2
100=x^2+4+2x+x^2
100=2x^2+2x+4
50=x^2+x+2
X^2+x-48=0
(X+7)(x-6)=0
X=6 x=-7
you can do the math: x^2 + (x+2)^2 = 10^2
or you can recall your basic 3-4-5 right triangle and then just double all the sides.
To find the value of x, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, we have:
x^2 + (x+2)^2 = 10^2
Expanding the equation:
x^2 + x^2 + 4x + 4 = 100
Combining like terms:
2x^2 + 4x + 4 = 100
Subtracting 100 from both sides:
2x^2 + 4x - 96 = 0
Dividing both sides by 2 to simplify the equation:
x^2 + 2x - 48 = 0
Factoring the quadratic equation:
(x + 8)(x - 6) = 0
Setting each factor equal to zero:
x + 8 = 0 or x - 6 = 0
Solving for x:
x = -8 or x = 6
Since the length of a side cannot be negative, we discard the solution x = -8.
Therefore, the value of x is 6 cm.
To find the value of x, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Given that the hypotenuse is 10 cm long, we can set up the equation:
x^2 + (x + 2)^2 = 10^2
Expanding:
x^2 + (x^2 + 4x + 4) = 100
Combining like terms:
2x^2 + 4x + 4 = 100
Rearranging the equation to make it a quadratic equation:
2x^2 + 4x - 96 = 0
Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. For simplicity, we will use factoring:
2(x^2 + 2x - 48) = 0
(x + 8)(x - 6) = 0
Setting each factor equal to zero:
x + 8 = 0 or x - 6 = 0
From the first equation, x = -8 is not a valid solution.
From the second equation, x = 6.
Therefore, the value of x is 6 cm.