Question

Find the perimeter of square below which has a diagonal with a length of 14 cm. Write yeur answer in simplest radical form.

Answer 1

28√2

Explanation:

Since we have a square, the diagonal bisects the two 90-degree angles creating a 45 - 45 - 90 triangle. In this triangle, two sides are the same. Let's call them x. Now the hypotenuse of such a triangle would then be x times √2. Let's use this in our question. The diagonal is 14 cm. This means that x√2 = 14, because it is the hypotenuse of the 45-45-90 triangle. We will divide to isolate x, and get 14/√2

To rationalize, we multiply the top and bottom by √2, getting (14√2)/(√2 times √2)

Simplify:

(14√2)/2

Simplify:

7√2

This is one side. The perimeter will be 4 times this, so 28√2

Answer 2

Answer: 28sqrt(2) cm

Step-by-step explanation: In a square, the diagonal is the hypotenuse of a right triangle whose legs are the sides of the square. Let s be the length of one side of the square. Then, by the Pythagorean theorem, we have:

s^2 + s^2 = 14^2

Simplifying this equation, we get:

2s^2 = 196

Dividing both sides by 2, we get:

s^2 = 98

Taking the square root of both sides, we get:

s = sqrt(98) = sqrt(2 x 49) = 7sqrt(2)

Therefore, the perimeter of the square is:

4s = 4 x 7sqrt(2) = 28sqrt(2) cm

Hence, the perimeter of the square is 28sqrt(2) cm in simplest radical form.