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 15: Find the Missing Measurement for the Figure
#### Problem Statement:
You are given a right triangle with the following measurements:
- One leg is labeled as \( \frac{10}{3} \) meters.
- The hypotenuse is labeled as \( \frac{25}{4} \) meters.
#### Figure Description:
The right triangle diagram is shown with:
- The vertical leg labeled as \( \frac{10}{3} \) meters.
- The hypotenuse labeled as \( \frac{25}{4} \) meters.
- The horizontal leg is missing and labeled as \( h \).
#### Answer Choices:
a) 3.74 m
b) 3.75 m
c) 3.34 m
d) 1.88 m
#### Analysis:
To find the missing measurement \( h \), use the Pythagorean Theorem \( a^2 + b^2 = c^2 \), where \( a \) and \( b \) are the legs of the right triangle, and \( c \) is the hypotenuse.
Given:
- \( a = \frac{10}{3} \)
- \( c = \frac{25}{4} \)
Calculate \( h \):
\[ h^2 + \left(\frac{10}{3}\right)^2 = \left(\frac{25}{4}\right)^2 \]
#### Detailed Calculation:
\[ h^2 + \frac{100}{9} = \frac{625}{16} \]
Clear the fractions by finding a common denominator:
\[ h^2 + \frac{1600}{144} = \frac{5625}{144} \]
Subtract \(\frac{1600}{144}\) from both sides:
\[ h^2 = \frac{5625}{144} - \frac{1600}{144} \]
\[ h^2 = \frac{4025}{144} \]
Simplify the fraction:
\[ h^2 = \frac{805}{28.8} \]
\[ h = \sqrt{\frac{4025}{144}} \]
\[ h = 4.72 \, \text{meters} \]
However, none of the answer choices match this result. Recheck the math or consider approximation if necessary.
Correct the potential mistake and retest each answer:
\[ \sqrt{\frac{4025}{144}} \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f1b5800-f045-4ccc-a00d-a1a031eae7ac%2F30f1321a-ef7c-42a9-af36-c83486bde3fc%2Fajpr2ug_processed.jpeg&w=3840&q=75)
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