Question

A square has side length 10 yd. What is the length of a diagonal of the square?

Express in simplest radical form.

Answer 1

The length of a diagonal of a square with side length 10 yd is found using the Pythagorean theorem, resulting in the diagonal measuring 10√2 yd in simplest radical form.

Step-by-step explanation:

To find the length of a diagonal of a square with side length 10 yd, we can use the Pythagorean theorem. A square can be divided into two right-angled triangles, and the diagonal is the hypotenuse of these triangles. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). The formula is c^2 = a^2 + b^2. In our case, both a and b are equal to the side length of the square, which is 10 yd.

Now, the equation will look like this:

• c^2 = (10 yd)^2 + (10 yd)^2
• c^2 = 100 yd^2 + 100 yd^2
• c^2 = 200 yd^2
• c = √(200 yd^2)
• c = √(100 yd^2 * 2)
• c = √(100) * √(2) yd
• c = 10√2 yd

So, the length of the diagonal in simplest radical form is 10√2 yd.

Answer 2

10√2

Step-by-step explanation:

Lets cut the square into a triangle, making a line from one corner to another, then let's see what we have.

We shoupd have a triangle where we don't know the hypotenuse, which we can find using the formula: a^2 + b^2 = c^2

so:

10^2 + 10^2 = c^2

100 + 100 = c^2

c^2 = 200

now let's square root what we got

√200

there are 2 10's in 200, which will turn the equation to:

10√2

this can't be simplified further, so our answer is 10√2