If a right triangle has legs measuring 10 cm and 24 cm, how long is the hypotenuse?(1 point)
To find the length of the hypotenuse in a right triangle, you can use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the two legs. Therefore, in this case, the hypotenuse can be found by calculating the square root of (10^2 + 24^2) which equals 26 cm.
To find the length of the hypotenuse in a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's label the legs of the triangle as side A and side B, and the hypotenuse as side C.
Given:
Side A = 10 cm
Side B = 24 cm
Using the Pythagorean theorem, we can write the equation:
A^2 + B^2 = C^2
Substitute the values:
10^2 + 24^2 = C^2
Perform the calculations:
100 + 576 = C^2
676 = C^2
Now, find the square root of both sides to solve for C:
√676 = √C^2
26 = C
Therefore, the length of the hypotenuse is 26 cm.
To find the length of the hypotenuse 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.
Let's use this theorem to solve the problem:
Step 1: Identify the lengths of the two legs of the right triangle.
Given that the legs of the right triangle measure 10 cm and 24 cm.
Step 2: Apply the Pythagorean theorem.
According to the Pythagorean theorem, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the two legs (a and b).
So, c^2 = a^2 + b^2.
Step 3: Substitute the values into the equation.
In our case, a = 10 cm and b = 24 cm. Plugging these values into the equation gives us:
c^2 = 10^2 + 24^2.
Step 4: Simplify the equation.
Calculating the squares gives us:
c^2 = 100 + 576.
Adding the two values together, we have:
c^2 = 676.
Step 5: Take the square root of both sides.
To find the length of the hypotenuse (c), we need to take the square root of both sides of the equation:
√(c^2) = √676.
Simplifying this gives us:
c = 26 cm.
So, the length of the hypotenuse is 26 cm.