Question

3.4.3 Quiz: Special Right Triangles

What is the length of sides of the square shown below?

45

8

90⁰

S

OA. 4√2

OB. 1

OC. 2

OD. √

OE. 8-√2

OF. 4

Answer 1

To find the length of the sides of the square, we can use the Pythagorean theorem. The length of each side of the square is 4(sqrt(2)).

Step-by-step explanation:

To find the length of the sides of the square, we need to use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. Since the square is made up of two congruent right triangles, we can use the Pythagorean theorem to find the length of the sides of the square.

Let x be the length of each leg of the square. Using the Pythagorean theorem, we have x^2 + x^2 = (sqrt(2)x)^2. Simplifying this equation, we get 2x^2 = 2x^2. This means that x^2 = x^2, so x = sqrt(2).

Therefore, the length of each side of the square is 4(sqrt(2)). Answer choice OA is correct.

Answer 2

The length of the sides of the square is 4√2.

Step-by-step explanation:

The length of the sides of the square shown below can be found using a special right triangle. Since the square is a right triangle, we can use the Pythagorean theorem to find the length of the sides. 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, the hypotenuse of the triangle is equal to the length of the side of the square. Let's denote it as 'a'. The other two sides are equal in length and let's denote them as 'b'. Since the sides of the square are congruent, the equation becomes: a^2 = b^2 + b^2. Simplifying this equation gives us a^2 = 2b^2.

Taking the square root of both sides, we get: a = sqrt(2b^2) = b sqrt(2). Therefore, the length of the side of the square is 4√2.