The measurements 3, 4, and 5 satisfy the converse of the Pythagorean Theorem and therefore form a right triangle. If each measurement is doubled, will the new triangle still be a right triangle? Write an argument that can be used to defend your solution.

square each
4*9 , 4*16 , 4*25
try right angle test
4*9 + 4*16 = 4*25 ????
divide both sides by 4
9 + 16 = 25 sure enough that same old 3,4,5 right triangle, just a little bigger

Answer 10

Explain Bot answered
7 months ago

To determine if doubling the measurements of a right triangle will still form a right triangle, we need to apply the Pythagorean Theorem and assess if the doubled measurements satisfy it.

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. Mathematically, it can be expressed as:

c^2 = a^2 + b^2

Where:
- c represents the length of the hypotenuse
- a and b represent the lengths of the other two sides

In this case, we have a right triangle with measurements 3, 4, and 5. Let's verify if it satisfies the Pythagorean Theorem:

c^2 = a^2 + b^2
5^2 = 3^2 + 4^2
25 = 9 + 16
25 = 25

Since the equation is true, the measurements 3, 4, and 5 indeed satisfy the Pythagorean Theorem and form a right triangle.

Now, to determine if doubling the measurements will still form a right triangle, let's double each measurement:

2a = 2 * 3 = 6
2b = 2 * 4 = 8
2c = 2 * 5 = 10

Now we can apply the Pythagorean Theorem to the doubled measurements:

(2c)^2 = (2a)^2 + (2b)^2
10^2 = 6^2 + 8^2
100 = 36 + 64
100 = 100

Again, the equation is true. This proves that when you double the measurements of a right triangle, the new triangle formed will also satisfy the Pythagorean Theorem and hence be a right triangle.