Question

Given a square with a diagonal of 20. Find the length of a side in simplest radical form.

a) 10
b) 10√2
c) 20
d) 20√2

Answer 1

The length of a side in a square with a diagonal of 20 is 10√2.

Step-by-step explanation:

Given a square with a diagonal of 20, we can use the Pythagorean theorem to find the length of a side. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (diagonal in this case) is equal to the sum of the squares of the other two sides. Since a square has four equal sides, we can let the length of a side be 'x'.

Using the Pythagorean theorem, we have:

x^2 + x^2 = 20^2

2x^2 = 400

x^2 = 200

x = √200 = √(100 * 2) = 10√2

Therefore, the length of a side of the square is 10√2.