Unit 7 Polygons and Quadrilaterals Homework 3 Rectangles Answer Key
Introduction
In Unit 7 of your geometry class, you have been learning about polygons and quadrilaterals. As part of your homework, you were assigned Homework 3, which specifically focused on rectangles. In this article, we will provide you with the answer key to Homework 3, helping you understand and check your answers.
Understanding Rectangles
Before we dive into the answer key, let's quickly review what a rectangle is. A rectangle is a type of quadrilateral with four right angles. It is also a special type of parallelogram, as it has opposite sides that are parallel and congruent. The opposite sides of a rectangle are also perpendicular to each other.
Question 1: Finding the Perimeter
In this question, you are asked to find the perimeter of a rectangle with a length of 12 units and a width of 6 units. To find the perimeter of a rectangle, you can use the formula P = 2(l + w), where P represents the perimeter, l represents the length, and w represents the width. Plugging in the given values, we get P = 2(12 + 6) = 2(18) = 36 units. Therefore, the perimeter of the rectangle is 36 units.
Question 2: Finding the Area
In Question 2, you are tasked with finding the area of a rectangle with a length of 8 units and a width of 5 units. The formula to find the area of a rectangle is A = l * w, where A represents the area, l represents the length, and w represents the width. Substituting the given values, we get A = 8 * 5 = 40 square units. Hence, the area of the rectangle is 40 square units.
Question 3: Finding the Diagonal
For Question 3, you need to determine the length of the diagonal of a rectangle with a length of 10 units and a width of 6 units. To find the length of the diagonal, you can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the length and width of the rectangle form the two sides of the right triangle, and the diagonal is the hypotenuse. Plugging in the values, we have d^2 = 10^2 + 6^2 = 100 + 36 = 136. Taking the square root of both sides, we find that the diagonal is approximately 11.66 units.
Question 4: Finding the Missing Side Length
In Question 4, you are given a rectangle with a length of 15 units and a diagonal of 17 units. You are asked to find the width of the rectangle. To solve this problem, we can use the Pythagorean theorem again. Let's assume the width is represented by w. We can set up the equation as follows: 15^2 + w^2 = 17^2. Simplifying this equation, we have 225 + w^2 = 289. Subtracting 225 from both sides, we get w^2 = 64. Taking the square root of both sides, we find that the width is 8 units.
Question 5: Determining the Perimeter Given the Area
For Question 5, you are given the area of a rectangle, which is 48 square units, and one side length, which is 6 units. You need to find the perimeter of the rectangle. Since the formula to find the area of a rectangle is A = l * w, we can rearrange the formula to solve for the missing side length. Dividing both sides of the equation by the given length, we have w = A / l = 48 / 6 = 8 units. Now that we know the width, we can use the perimeter formula to find the perimeter. Plugging in the values, we get P = 2(6 + 8) = 2(14) = 28 units. Therefore, the perimeter of the rectangle is 28 units.
Question 6: Determining the Missing Angle
Question 6 involves finding the measure of a missing angle in a rectangle. You are given that one angle measures 80 degrees. Since all angles in a rectangle are right angles, which measure 90 degrees, we can subtract the given angle from 90 to find the missing angle. Subtracting 80 from 90, we get 10 degrees. Therefore, the missing angle measures 10 degrees.
Question 7: Determining the Missing Side Length Given the Perimeter
For the final question, you are given the perimeter of a rectangle, which is 36 units, and one side length, which is 10 units. You need to find the length of the missing side. We can start by using the perimeter formula to find the sum of the lengths of the two sides we know. Plugging in the values, we have 36 = 2(10 + w), where w represents the missing side length. Simplifying this equation, we get 36 = 20 + 2w. Subtracting 20 from both sides, we have 16 = 2w. Dividing both sides by 2, we find that the missing side length is 8 units.
Conclusion
By reviewing the answer key provided for Homework 3 on rectangles, you should now have a better understanding of how to solve various problems related to rectangles. Remember to always use the appropriate formulas and concepts to find the correct answers. Keep practicing and exploring the world of polygons and quadrilaterals to strengthen your geometry skills!