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.
![**Problem Statement:**
Given: \( \triangle EDC \) is similar to \( \triangle ABC \). Solve for \( x \).
**Solution:**
The key to solving this problem lies in understanding the property of similar triangles, where the corresponding sides have proportional lengths.
Given:
- \( \triangle EDC \) and \( \triangle ABC \) are similar.
- The sides of \( \triangle ABC \) are \( AB = 6 \, \text{m} \) and \( BC = 12.5 \, \text{m} \).
- The sides of \( \triangle EDC \) are \( ED = x \, \text{m} \) and \( DC = 4 \, \text{m} \).
**Steps to solve for \( x \):**
Since the triangles are similar:
\[ \frac{ED}{AB} = \frac{DC}{BC} \]
Plugging in the known values:
\[ \frac{x}{6} = \frac{4}{12.5} \]
Cross-multiplying to solve for \( x \):
\[ x = \frac{4 \cdot 6}{12.5} \]
\[ x = \frac{24}{12.5} \]
Simplifying:
\[ x = 1.92 \]
Therefore, the value of \( x \) is:
\[ x = 1.92 \, \text{m} \]
[ **Answer: \( x = 1.92 \, \text{m} \) **]
**Explanation of the Diagram:**
- The diagram depicts two right-angled triangles, \( \triangle ABC \) and \( \triangle EDC \).
- \( \triangle ABC \) is the larger triangle with a right angle at \( B \), and sides:
- \( AB = 6 \, \text{m} \) (vertical side)
- \( BC = 12.5 \, \text{m} \) (diagonal side)
- \( \triangle EDC \) is the smaller triangle with a right angle at \( D \), and sides:
- \( ED = x \, \text{m} \) (vertical side)
- \( DC = 4 \, \text{m} \) (horizontal side)
This detailed explanation provides the necessary steps to find the value of \( x \) using](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0b3aeb85-845c-4897-8321-5d700bdd20c9%2Fff6870c1-ee0f-49ce-89ae-af85595abd6a%2F01ofem_processed.png&w=3840&q=75)
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