6.
The length of the hypotenuse of a right triangle is 15 cm. The length of one leg is 9 cm. Find the length of the other leg.
6 cm
12 cm
17 cm
144 cm
Use the Pythagorean Theorem.
a^2 + b^2 = c^2
a^2 + 9^2 = 15^2
Solve for a.
9^2 + x^2 = 15^2
81 + x^2 = 225
x^2 = 144
x = 12
or, since you are familiar with the 3-4-5 right triangle, you might have noticed that
9 = 3x3
15 = 3x5
so the other leg would be 3x4 = 12
To find the length of the other leg in a right triangle, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this problem, we are given the length of the hypotenuse, which is 15 cm, and one leg, which is 9 cm.
Step 1: Write down the Pythagorean theorem:
c^2 = a^2 + b^2
where c is the length of the hypotenuse and a and b are the lengths of the other two sides.
Step 2: Plug in the given values:
15^2 = 9^2 + b^2
Step 3: Simplify the equation:
225 = 81 + b^2
Step 4: Simplify further:
225 - 81 = b^2
144 = b^2
Step 5: Take the square root of both sides to solve for b:
√144 = √(b^2)
12 = b
Therefore, the length of the other leg is 12 cm.
To find the length of the other leg of a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem 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 are given the length of the hypotenuse (15 cm) and one leg (9 cm). Let's call the length of the other leg "x".
Using the Pythagorean theorem, we can write the equation:
9^2 + x^2 = 15^2
Simplifying the equation, we have:
81 + x^2 = 225
Next, we can solve for x by subtracting 81 from both sides:
x^2 = 225 - 81
x^2 = 144
To find the value of x, we take the square root of both sides:
x = sqrt(144)
x = 12
Therefore, the length of the other leg is 12 cm.
So, the correct answer is 12 cm.