Find the value of x in the right triangle
x◣x+1
7
Nice graphic
(x+1)^2 = x^2 + 7^2
x^2 + 2x + 1 = x^2 + 49
2x = 48
x = 24
check:
25^2 = 625
24^2 + 7^2 = 576+48= 625 , yeahh
To find the value of x in the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, 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 two legs of the right triangle as x and x + 1, and the hypotenuse is 7.
According to the Pythagorean theorem:
x^2 + (x+1)^2 = 7^2
Simplifying the equation:
x^2 + (x^2 + 2x + 1) = 49
Combine like terms:
2x^2 + 2x + 1 = 49
Rearrange the equation to bring all terms to one side:
2x^2 + 2x + 1 - 49 = 0
2x^2 + 2x - 48 = 0
Now, we have a quadratic equation. To solve it, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our quadratic equation, a = 2, b = 2, and c = -48. Substituting these values into the quadratic formula:
x = (-2 ± √(2^2 - 4*2*(-48))) / (2*2)
Simplifying further:
x = (-2 ± √(4 + 384)) / 4
x = (-2 ± √388) / 4
Now, we calculate the square root:
x = (-2 ± 19.7) / 4
This gives us two possible solutions:
x = (-2 + 19.7) / 4 ≈ 4.18
x = (-2 - 19.7) / 4 ≈ -5.92
Therefore, the possible values of x in the right triangle are approximately 4.18 and -5.92.