Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter10: Measurement, Area, And Volume
Section10.1: Triangles
Problem 1C
Related questions
Question
![**Question:**
The hypotenuse of a 45°-45°-90° triangle measures \(7\sqrt{2}\) units. What is the length of one leg of the triangle?
**Diagram Explanation:**
The diagram shows an isosceles right triangle (45°-45°-90° triangle). In this particular triangle:
- The two legs, which are of equal length, form the right angle.
- The hypotenuse, opposite the right angle, is labeled \(7\sqrt{2}\) units.
**Options:**
1. 7 units
2. \(7\sqrt{2}\) units
3. 14 units
4. \(14\sqrt{2}\) units
**Explanation:**
In a 45°-45°-90° triangle, the hypotenuse is \( \sqrt{2} \) times the length of each leg. Given the hypotenuse is \( 7\sqrt{2} \) units, we can find the length of one leg by dividing the length of the hypotenuse by \( \sqrt{2} \):
\[
\text{Leg length} = \frac{7\sqrt{2}}{\sqrt{2}} = 7 \text{ units}
\]
The correct answer is:
- 7 units](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1fefc4e4-0fc1-4d3a-92e0-1dd9cbc9acda%2F6a61e8ad-7b8e-48f1-982d-f9ec30a56dad%2F5m1weyj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
The hypotenuse of a 45°-45°-90° triangle measures \(7\sqrt{2}\) units. What is the length of one leg of the triangle?
**Diagram Explanation:**
The diagram shows an isosceles right triangle (45°-45°-90° triangle). In this particular triangle:
- The two legs, which are of equal length, form the right angle.
- The hypotenuse, opposite the right angle, is labeled \(7\sqrt{2}\) units.
**Options:**
1. 7 units
2. \(7\sqrt{2}\) units
3. 14 units
4. \(14\sqrt{2}\) units
**Explanation:**
In a 45°-45°-90° triangle, the hypotenuse is \( \sqrt{2} \) times the length of each leg. Given the hypotenuse is \( 7\sqrt{2} \) units, we can find the length of one leg by dividing the length of the hypotenuse by \( \sqrt{2} \):
\[
\text{Leg length} = \frac{7\sqrt{2}}{\sqrt{2}} = 7 \text{ units}
\]
The correct answer is:
- 7 units
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