TEKS 8.7A Worksheets — Grade 8 Use the Pythagorean Theorem and its converse

During a school field trip to the San Antonio River Walk, Priya and her friends are exploring the area. They notice a beautiful right triangle garden design where the length of one leg is 6 meters and the length of the other leg is 8 meters. What is the length of the diagonal path (the hypotenuse) that cuts across the garden in meters?

1. 10 ✓
2. 12
3. 14
4. 9

Why: To find the length of the diagonal path (the hypotenuse), we can use the Pythagorean Theorem, which states a² + b² = c², where c is the hypotenuse. Here, a is 6 meters and b is 8 meters. So, we calculate 6² + 8² = 36 + 64 = 100. Then, we find c by taking the square root of 100, which gives us c = 10 meters. Therefore, the length of the diagonal path is 10 meters.

Maria is making a triangular banner for a festival in West, Texas. The two legs of the triangle are 6 feet and 8 feet long. To find the hypotenuse of the triangle, how long does Maria need to make the banner?

1. 10 ✓
2. 12
3. 14
4. 16

Why: To find the length of the hypotenuse, use the Pythagorean theorem, a² + b² = c². Here, a = 6 feet and b = 8 feet. So, calculate 6² + 8² = 36 + 64 = 100. Then find c by taking the square root of 100, which equals 10 feet. Therefore, Maria needs to make the banner 10 feet long.

Maria is helping her uncle at his ranch in Amarillo. He has a rectangular pasture that measures 80 yards in length and 60 yards in width. He wants to put up a fence that runs diagonally across the pasture to create two triangular sections. What is the length of the fence he needs to install, rounded to the nearest yard?

1. 100 ✓
2. 120
3. 140
4. 60

Why: To find the length of the fence that runs diagonally across the rectangular pasture, we can use the Pythagorean Theorem. The formula is a² + b² = c², where 'a' and 'b' are the legs of the right triangle (the length and width of the pasture) and 'c' is the hypotenuse (the diagonal fence). Here, a = 80 yards and b = 60 yards. So, we calculate: c² = 80² + 60² = 6400 + 3600 = 10000. Taking the square root gives us c = √10000 = 100 yards. Therefore, the length of the fence needed is 100 yards.

Hana is helping her grandmother plant a new garden in their backyard in McAllen, Texas. The garden will be in the shape of a right triangle where one leg measures 6 feet and the other leg measures 8 feet. To determine how much fencing she needs to buy to enclose the garden, Hana needs to find the length of the hypotenuse. What is the length of the hypotenuse, rounded to the nearest tenth of a foot?

1. 10.0 ✓
2. 12.0
3. 14.0
4. 8.0

Why: To find the length of the hypotenuse in a right triangle, we use the Pythagorean Theorem, which states that a² + b² = c², where c is the hypotenuse. Here, the lengths of the legs are 6 feet and 8 feet. We calculate as follows: 6² + 8² = 36 + 64 = 100. Now take the square root of 100, which gives us c = 10. Therefore, the length of the hypotenuse is 10.0 feet.

Cristian wants to build a small wooden shed in his backyard in Lubbock, Texas. He decides to make the shed in the shape of a right triangle. The two legs of the triangle will be 6 feet and 8 feet long. To find out how much wood he needs for the diagonal support beam, which represents the hypotenuse of the triangle, what is the length of the hypotenuse in feet?

1. 10 ✓
2. 14
3. 8
4. 6

Why: To find the length of the hypotenuse in a right triangle, we use the Pythagorean Theorem, which is a² + b² = c². Here, a = 6 and b = 8. So, we calculate: 6² + 8² = 36 + 64 = 100. To find c, we take the square root of 100, which is 10. Therefore, the length of the hypotenuse is 10 feet.

Lily is designing a habitat for a school project on Texas wildlife. She wants to create a right triangle shaped area for a display about the great horned owl. The base of the triangle will be 12 feet long, and the height of the triangle will be 16 feet. What is the length of the hypotenuse of the triangle, which represents the diagonal support needed for the structure?

1. 20 feet ✓
2. 18 feet
3. 15 feet
4. 14 feet

Why: To find the length of the hypotenuse in a right triangle, we use the Pythagorean Theorem, which states that a² + b² = c², where c is the hypotenuse. In this problem, a is 12 and b is 16. First, calculate 12² + 16²: 144 + 256 = 400. Now, take the square root of 400, which is 20. Therefore, the length of the hypotenuse is 20 feet.

Kayla is building a birdwatching platform in her backyard for the Texas birds she loves to observe. She wants to create a right triangle with her platform setup. The base of the platform will be 6 feet long, and the height will be 8 feet high. What is the length of the diagonal support beam she will need to secure the platform? Use the Pythagorean Theorem to find the length.

1. 10 feet ✓
2. 14 feet
3. 12 feet
4. 8 feet

Why: To find the length of the diagonal support beam, we can apply the Pythagorean Theorem, which states that a² + b² = c², where 'c' is the hypotenuse (the diagonal support), and 'a' and 'b' are the other two sides of the right triangle. Here, a = 6 feet and b = 8 feet. First, we calculate a² + b²: 6² + 8² = 36 + 64 = 100. Now, we find c by taking the square root of 100, which is 10 feet. Therefore, the length of the diagonal support beam is 10 feet.

Levi is building a garden in his backyard that will be in the shape of a right triangle. One leg of the triangle measures 6 feet, and the other leg measures 8 feet. How long is the diagonal that connects the two legs, which represents the hypotenuse of the triangle?

1. 10 ✓
2. 14
3. 36
4. 40

Why: To find the length of the hypotenuse in a right triangle, we can use the Pythagorean Theorem, which states that a² + b² = c², where c is the hypotenuse. Here, a is 6 feet and b is 8 feet. First, we calculate 6² + 8² = 36 + 64 = 100. Now we find the square root of 100, which gives us c = 10 feet. Therefore, the length of the hypotenuse is 10 feet.