Question

A square has an area of 44.89 inches squared. How do I get the length of the diagonal?

Answer 1

6.7√2 in ≈ 9.48 in

Explanation:

First, use the area of the square to find the side length.

A = s²

44.89 in² = s²

s = 6.7 in

The diagonal of a square divides it into 45-45-90 triangles. You can use Pythagorean theorem to find the length of the diagonal.

c² = a² + b²

c² = (6.7 in)² + (6.7 in)²

c = 6.7√2 in

c ≈ 9.48 in

Answer 2

Answer: 6.7√2

Step-by-step explanation: Let's start this problem by drawing a picture of a square with a diagonal of length x.

Now to find the length of the diagonal, let's first find the length of a side of the square. To find the length of a side, remember that the formula for the area of a square is S² and since we know that the area of the given square is 44.89 inches, we can set up the equation 44.89 = S².

Square rooting both sides, we have 6.7 = S so we can give the side of our square a length of 6.7. Now to find the value of x, it's important to understand that the diagonal of a square creates 45° 45° 90° triangles and in a 45° 45° 90° triangle, the hypotenuse = √2 × leg.

So we have x = 6.7√2.

So the length of the diagonal of the square is 6.7√2 inches.

Image provided.