Respuesta :
Answer:
6.7√2 in ≈ 9.48 in
Step-by-step 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: 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.