The Pythagorean Theorem is modeled below. Square 1 has a perimeter of 12 units and Square 2 has a perimeter of 16 units.
The Pythagorean Theorem is modeled below. Square 1 has a perimeter of 12 units and Square 2 has a perimeter of 16 units.
What is the area of Square 3?
F.20 square units
G.25 square units
H.100 square units
J.625 square units
so #1 has a side of 3
and #2 has a side of 4
You haven't asked a question, but does 3-4-5 sound familiar?
The Pythagorean Theorem is modeled below. Square 1 has a perimeter of 12 units and Square 2 has a perimeter of 16 units.
What is the area of Square 3?
F.20 square units
G.25 square units
H.100 square units
J.625 square units
whats the answer
25 bozo
F.20 square units
To understand how the Pythagorean Theorem can be applied in this situation, let's first review the theorem itself. The Pythagorean Theorem states that 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 other two sides.
In this case, Square 1 and Square 2 are used to model a right triangle. Let's label the sides of the right triangle as follows:
- Side 1: The length of a side of Square 1.
- Side 2: The length of a side of Square 2.
- Hypotenuse: The length of the hypotenuse of the right triangle.
Based on the given information, we can deduce the following:
Square 1 has a perimeter of 12 units, which means that the sum of all four sides of Square 1 is 12 units. Since Square 1 is a square, all sides are equal in length. Therefore, the length of each side of Square 1 is 12 divided by 4, which is 3 units.
Square 2 has a perimeter of 16 units, which means that the sum of all four sides of Square 2 is 16 units. Again, since Square 2 is a square, all sides are equal in length. Therefore, the length of each side of Square 2 is 16 divided by 4, which is 4 units.
Now that we know the lengths of Side 1 and Side 2, we can use the Pythagorean Theorem to find the length of the hypotenuse. By substituting the values into the theorem, we get the following equation:
Side 1^2 + Side 2^2 = Hypotenuse^2
(3 units)^2 + (4 units)^2 = Hypotenuse^2
9 units^2 + 16 units^2 = Hypotenuse^2
25 units^2 = Hypotenuse^2
To solve for the Hypotenuse, we take the square root of both sides of the equation:
√(25 units^2) = √(Hypotenuse^2)
5 units = Hypotenuse
Therefore, the length of the hypotenuse is 5 units.