If I told you a triangle with sides 45 cm, 60 cm, and 75 cm was a right triangle, how would you verify my statement? Develop an argument to convince yourself and your partner that my statement is correct.
it's just a scaled-up 3-4-5 right triangle.
You can check to see whether 45^2 + 60^2 = 75^2
it does
45^2 + 60^2 = 75^2 ??
2025 + 3600 = 5625
5625 = 5625
Yes! The Pythagorean Theorem proves it's a right triangle.
I know that a 3, 4 , 5 triangle is a right triangle
but I can prove it easily anyway because
9 + 16 = 25 or in other words a^2+b^2=c^2
now multiply each side by 15 and get
45, 60 , 75 :)
To verify whether the triangle with sides measuring 45 cm, 60 cm, and 75 cm is indeed a right triangle, we can apply the Pythagorean theorem. 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.
So, let's calculate the squares of the lengths of all three sides:
- Side 1: 45 cm^2 = 2025 cm^2
- Side 2: 60 cm^2 = 3600 cm^2
- Side 3: 75 cm^2 = 5625 cm^2
Now, let's check if the sum of the squares of the two smaller sides equals the square of the longest side:
2025 cm^2 + 3600 cm^2 = 5625 cm^2
The sum of the squares of the two smaller sides is indeed equal to the square of the longest side. Therefore, based on the Pythagorean theorem, the triangle with sides measuring 45 cm, 60 cm, and 75 cm satisfies the condition for being a right triangle.
To convince your partner of the validity of this argument, you can present the evidence of the calculations that demonstrate the relationship between the side lengths and the Pythagorean theorem. Sharing your step-by-step thought process and calculations will further support your argument.