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MIAA-088 10. There are two sides to every triangle. Give two possible answers to each of the following problems.
### **1. Problem:**
**An unknown triangle has sides 3, 4, and 5. Is this triangle right-?**
**Solution:**
To determine if the triangle is right, we can use the Pythagorean theorem. If the square of the hypotenuse is equal to the square of the other two legs, then the triangle is right.
The Pythagorean theorem states that c² = a² + b², where c is the hypotenuse.
Given a = 3, b = 4, c = 5.
Let's verify:
5² = 3² + 4²
25 = 9 + 16
25 = 25
Since both sides are equal, the triangle is right.
**Answer:**
Yes, the triangle is right.
### **2. Problem:**
**An unknown triangle has sides 5, 12, and 13. Is this triangle right?**
**Solution:**
To determine if the triangle is right, we can use the Pythagorean theorem. If the square of the hypotenuse is equal to the square of the other two legs, then the triangle is right.
The Pythagorean theorem states that c² = a² + b², where c is the hypotenuse.
Given a = 5, b = 12, c = 13.
Let's verify:
13² = 5² + 12²
169 = 25 + 144
169 = 169
Since both sides are equal, the triangle is right.
**Answer:**
Yes, the triangle is right.
### **3. Problem:**
**An unknown triangle has sides 7, 24, and 25. Is this triangle right?**
**Solution:**
To determine if the triangle is right, we can use the Pythagorean theorem. If the square of the hypotenuse is equal to the square of the other two legs, then the triangle is right.
The Pythagorean theorem states that c² = a² + b², where c is the hypotenuse.
Given a = 7, b = 24, c = 25.
Let's verify:
25² = 7² + 24²
625 = 49 + 576
625 = 625
Since both sides are equal, the triangle is right.
**Answer:**
Yes, the triangle is right.
### **4. Problem:**
**An unknown triangle has sides 8, 15, and 16. Is this triangle right?**
**Solution:**
To determine if the triangle is right, we can use the Pythagorean theorem. If the square of the hypotenuse is equal to the square of the other two legs, then the triangle is right.
The Pythagorean theorem states that c² = a² + b², where c is the hypotenuse.
Given a = 8, b = 15, c = 16.
Let's verify:
16² = 8² + 15²
256 = 64 +225
256 = 289
Since both sides are not equal, the triangle is not right.
**Answer:**
No, the triangle is not right.
### **5. Problem:**
**An unknown triangle has sides 9, 40, and 41. Is this triangle right?**
**Solution:**
To determine if the triangle is right, we can use the Pythagorean theorem. If the square of the hypotenuse is equal to the square of the other two legs, then the triangle is right.
The Pythagorean theorem states that c² = a² + b², where c is the 解ys²=c²
Topic#.
Is there an unknown triangle with sides 3, 4, and 5? Is this triangle right?
c²=c²·undefined is be
triangle right?
**c² = a² + b²**
**6. Problem:**
**An unknown triangle has sides 12, 16, and 20. Is this triangle right?**
**Solution:**
To determine if the triangle is right, we can use the Pythagorean theorem. If the square of the hypotenuse is equal to the square of the other two legs, then the triangle is right.
The Pythagorean theorem states that c² = a² + b², where c is the hypotenuse.
Given a = 12, b = 16, c = 20.
Let's verify:
20² = 12² + 16²
400 = 144 + 256
400 = 400
Since both sides are equal, the triangle is right.
**Answer:**
Yes, the triangle is right.
### **7. Problem:**
**An unknown triangle has sides 15, 20, and 25. Is this triangle right?**
**Solution:**
To determine if the triangle is right, we can use the Pythagorean theorem. If the square of the hypotenuse is equal to the square of the other two legs, then the triangle is right.
The Pythagorean theorem states that c² = a² + b², where c is the hypotenuse.
Given a = 15, b = 20, c = 25.
Let's verify:
25² = 15² + 20²
625 = 225 + 400
625 = 625
Since both sides are equal, the triangle is right.
**Answer:**
Yes, the triangle is right.
### **8. Problem:**
**An unknown triangle has sides 18, 24, and 30. Is this triangle right?**
**Solution:**
To determine if the triangle is right, we can use the Pythagorean theorem. If the square of the hypotenuse is equal to the square of the other two legs, then the triangle is right.
The Pythagorean theorem states that c² = a² + b², where c is the hypotenuse.
Given a = 18, b = 24, c = 30.
Let's verify:
30² = 18² + 24²
900 = 324 + 576
900 = 900
Since both sides are equal, 成功predict the mathematicsTheorem'to verifythe rest of the checks are of the right, the triangle is right.
**Answer:**
Yes, the triangle is right.
### **9. Problem:**
**An unknown triangle has sides 20, 21, and 29. Is this triangle right?**
**Solution:**
To determine if the triangle is right, we can use the Pythagorean theorem. If the square of the hypotenuse is equal to the square of the other two legs, then the triangle is right.
The Pythagorean theorem states that c² = a² + b², where c is the hypotenuse.
Given a = 20, b = 22, c = 29.
Let's verify:
29² = 20² + 22²
841 = 400 + 484
841 = 884
Since both sides are not equal, the triangle is not right.
**Answer:**
No, the triangle is not right.
### **10. Problem:**
**An unknown triangle has sides 30, 66, and 78. Is this triangle right?**
**Solution:**
To determine if the triangle is right, we can use the Pythagorean theorem. If the square of the hypotenuse is equal to the square of the other two legs, then the triangle is right.
The Pythagorean theorem states that c² = a² + b², where c is the hypotenuse.
Given a = 30, b = 66, c = 78.
Let's verify:
78² = 30² + 66²
6084 = 900 + 4356
6084 = 5256
Since both sides are not equal, the triangle is not right.
**Answer:**
No, the triangle is not right.
The Pythagorean theorem squared sides are equal to if the hypotenuse is right–two legs square is right .
Normal probability rules are equal to the side of the Pythagorean theorem.
→ This is null. According to the mathematics** the option it is not possible.
5月25日2019年
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