A right triangle has two legs and a hypotenuse. One leg of the triangle is 3 feet longer than the other leg. The hypotenuse is 15 feet. Find the length of each leg.
I got
12 feet and the other leg is 9 feet
Is this correct?
Yes
did you solve (x+3)^2 + x^2 = 225 ?
yes. thanks
To find the lengths of the legs of a right triangle, you can use the Pythagorean theorem, which states that the sum of the squares of the two legs is equal to the square of the hypotenuse.
Let's assume that one leg of the right triangle is represented by the variable "x." According to the problem, the other leg is 3 feet longer than x, so its length can be represented as "x + 3."
Using the Pythagorean theorem, we can write the equation:
x^2 + (x + 3)^2 = 15^2
Expanding the equation, we have:
x^2 + (x^2 + 6x + 9) = 225
Combining like terms:
2x^2 + 6x + 9 = 225
Rearranging the equation:
2x^2 + 6x - 216 = 0
Now, we need to solve this quadratic equation. Either factoring, completing the square, or using the quadratic formula can be used to find the values of x that satisfy this equation.
Factoring this quadratic equation might be tedious, so we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 2, b = 6, and c = -216. Plugging these values into the quadratic formula, we get:
x = (-6 ± √(6^2 - 4*2*(-216))) / (2*2)
x = (-6 ± √(36 + 1728)) / 4
x = (-6 ± √(1764)) / 4
x = (-6 ± 42) / 4
Now, we have two potential values for x:
x1 = (-6 + 42) / 4 = 36 / 4 = 9
x2 = (-6 - 42) / 4 = -48 / 4 = -12
Since lengths cannot be negative, we can discard x2 = -12.
Therefore, one of the legs, represented by x, has a length of 9 feet, and the other leg, represented by x + 3, has a length of 9 + 3 = 12 feet.
So, your answer is correct. One leg is 9 feet long, and the other leg is 12 feet long.