Answer:
246420.48 square units.
Explanation:
To find the area of the square that shares a side with the third side of the right triangle, we first need to determine the length of the third side.
In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This relationship is known as the Pythagorean theorem.
Using the given lengths of the two sides, we can apply the Pythagorean theorem to find the length of the third side:
(222)^2 + (444)^2 = c^2, where c is the length of the hypotenuse.
49284 + 197136 = c^2
c^2 = 246420
Taking the square root of both sides, we get:
c ≈ √246420 ≈ 496.41
Now that we have the length of the third side, which is approximately 496.41 units, we can find the area of the square that shares a side with this side. The area of a square is calculated by squaring the length of one of its sides.
Therefore, the area of the square is:
(496.41)^2 ≈ 246420.48 square units
So, the area of the square that shares a side with the third side of the right triangle is approximately 246420.48 square units.