11. Do the lengths 12, 12.2, and 6.4 form a right triangle? Justify your answer.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![### Question 11: Right Triangle Verification
**Problem Statement:**
Do the lengths 12, 12.2, and 6.4 form a right triangle? Justify your answer.
**Solution Explanation:**
To determine if three given lengths can form a right triangle, we use the Pythagorean theorem. This theorem states that for a right triangle, the sum of the squares of the two shorter sides must equal the square of the longest side (hypotenuse).
Given lengths: 12, 12.2, and 6.4
1. Identify the potential hypotenuse:
- The hypotenuse should be the longest side. In this case, 12.2 is the longest side.
2. Calculate the squares of the lengths:
- \(12^2 = 144\)
- \(6.4^2 = 40.96\)
- \(12.2^2 = 148.84\)
3. Verify the Pythagorean theorem:
- Sum of the squares of the two shorter sides:
\[
12^2 + 6.4^2 = 144 + 40.96 = 184.96
\]
- Compare this sum with the square of the hypotenuse:
\[
184.96 \neq 148.84
\]
Since \(184.96\) is not equal to \(148.84\), the given lengths do not satisfy the Pythagorean theorem. Therefore, the lengths 12, 12.2, and 6.4 do not form a right triangle.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F907aed91-1505-4072-81d2-6809179f9249%2Fe525106f-a50e-4d72-aa81-17dd85f7ae1f%2Fnq69nd_processed.jpeg&w=3840&q=75)
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