If one leg of a right triangle is 5 times the square root of 3 centimeters, and the hypotenuse is 2 more than the other leg, what is the length of the other leg?
While it does say please show my work, I literally have NO idea how to solve this, and this is one of my last questions to finish 10th grade..
it's a right triangle so use the Pythagorean Theorem. If the other leg is x, then
(5√3)^2 + x^2 = (x+2)^2
one leg is 5 sqrt 3
the other leg is x
the hypotenuse is x + 2
c^2 = a^2 + b^2
(x+2)^2 = x^2 + (5 rt3)^2
x^2 + 4x + 4 = x^2 + 75
4x + 4 =75 because the x^2 cancel.
Can you solve from here
Thank you both! Worked perfectly!
To solve this problem, we can start by assigning variables to the lengths of the legs of the right triangle.
Let's say:
One leg = x cm
The other leg = 5√3 cm
The hypotenuse = (5√3 + 2) cm
Now, according to the Pythagorean theorem, 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.
Using this theorem, we can form the following equation:
(x^2) + [(5√3)^2] = [(5√3 + 2)^2]
Simplifying this equation, we get:
x^2 + 75 = 75 + 20√3 + 4
Combining like terms, we have:
x^2 = 20√3 + 4
Now, to solve for x, we need to isolate it on one side of the equation. Since the right side of the equation does not contain x, we can subtract 4 from both sides:
x^2 - 4 = 20√3
Next, we can simplify the left side of the equation by factoring it as a difference of squares:
(x - 2)(x + 2) = 20√3
Now, divide both sides of the equation by (x + 2):
(x - 2)(x + 2)/(x + 2) = 20√3/(x + 2)
Simplifying further, we get:
x - 2 = 20√3/(x + 2)
Now, cross-multiply to eliminate the fractions:
(x - 2)(x + 2) = 20√3
Expanding the left side of the equation:
x^2 - 4 = 20√3
Finally, add 4 to both sides of the equation:
x^2 = 20√3 + 4
To find the value of x, we can take the square root of both sides:
x = √(20√3 + 4)
Now, we can use a calculator to find the approximate value of x.