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?
15^2=12^2+9^2
225=144+81
225=225
you are correct
To find the length of each leg of the right triangle, 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.
Let's assume the length of one leg is x, and since the other leg is 3 feet longer, its length would be x + 3.
Using the Pythagorean theorem, we have:
(x)^2 + (x + 3)^2 = (15)^2
Expanding and simplifying the equation:
x^2 + (x^2 + 6x + 9) = 225
Combining like terms:
2x^2 + 6x + 9 = 225
Rearranging the equation to isolate the quadratic terms:
2x^2 + 6x - 216 = 0
We can then solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Using the values from the quadratic equation, a = 2, b = 6, and c = -216:
x = (-6 ± √(6^2 - 4 * 2 * -216)) / (2 * 2)
Solving further:
x = (-6 ± √(36 + 1728)) / 4
x = (-6 ± √(1764)) / 4
x = (-6 ± 42) / 4
Now we have two possible values for x:
x = (-6 + 42) / 4 = 36 / 4 = 9
or
x = (-6 - 42) / 4 = -48 / 4 = -12
Since the length of a side cannot be negative, we discard the -12 value.
Thus, the length of one leg of the right triangle is 9 feet. Since the other leg is 3 feet longer, the length of the other leg is 9 + 3 = 12 feet.
Therefore, your answer is correct. The length of one leg is 9 feet, and the length of the other leg is 12 feet.