The length of the hypotenuse of a right triangle is 40 cm. The legs of the triangle are the same length. How long is each leg of the triangle?

Well, isn't that a right-angled pickle! If the hypotenuse is 40 cm, we can imagine each leg saying, "Hey, buddy, let's split this thing and split it in half!" So if we divide 40 cm by 2, we get 20 cm. Voilà! Each leg is 20 cm long.

To find the length of each leg of the right triangle, we can use the Pythagorean theorem. According to the theorem, the square of the hypotenuse is equal to the sum of the squares of the legs.

Let's assume that each leg of the right triangle has a length of 'x' cm.

Using the Pythagorean theorem, we can write the equation as:

x^2 + x^2 = 40^2

Simplifying the equation, we get:

2x^2 = 1600

Dividing both sides of the equation by 2:

x^2 = 800

Taking the square root of both sides to solve for 'x':

x = √800

Simplifying the square root, we get:

x ≈ 28.28 cm (rounded to two decimal places)

Therefore, each leg of the triangle is approximately 28.28 cm long.

To solve this problem, 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 two legs.

Let's assume the length of each leg of the triangle is "x" cm.

According to the problem, the length of the hypotenuse is 40 cm.

Using the Pythagorean Theorem, we can set up the following equation:

x^2 + x^2 = 40^2

Simplifying the equation, we get:

2x^2 = 1600

Dividing both sides of the equation by 2, we get:

x^2 = 800

To find the value of x, we take the square root of both sides of the equation:

x = √800

Simplifying the square root of 800, we get:

x ≈ 28.28

So, each leg of the triangle is approximately 28.28 cm long.

a^2 + b^2 = c^2

a^2 + a^2 = 40^2

2a^2 = 1,600

a^2 = 800

a = 28.28