Pythagorean Theorem
The Pythagorean Theorem, a fundamental principle in geometry attributed to the ancient Greek mathematician Pythagoras, posits a profound relationship between the sides of a right-angled triangle. It asserts that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This theorem not only serves as a cornerstone for mathematical theory and proof but also has practical applications in various fields such as architecture, engineering, and physics, illustrating the enduring influence of ancient mathematical discoveries on contemporary scientific and mathematical practices.
Questions
- An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of #4 # and the triangle has an area of #128 #. What are the lengths of sides A and B?
- A right triangle has sides A, B, and C. Side A is the hypotenuse and side B is also a side of a rectangle. Sides A, C, and the side of the rectangle adjacent to side B have lengths of #8 #, #2 #, and #14 #, respectively. What is the rectangle's area?
- A right triangle has sides A, B, and C. Side A is the hypotenuse and side B is also a side of a rectangle. Sides A, C, and the side of the rectangle adjacent to side B have lengths of #9 #, #3 #, and #3 #, respectively. What is the rectangle's area?
- A right triangle has sides A, B, and C. Side A is the hypotenuse and side B is also a side of a rectangle. Sides A, C, and the side of the rectangle adjacent to side B have lengths of #8 #, #5 #, and #22 #, respectively. What is the rectangle's area?
- A right triangle has sides A, B, and C. Side A is the hypotenuse and side B is also a side of a rectangle. Sides A, C, and the side of the rectangle adjacent to side B have lengths of #8 #, #7 #, and #14 #, respectively. What is the rectangle's area?
- If a triangle has a leg of 21 ft, and a hypotenuse of 35 ft, what is the measure of the other leg?
- An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of #9 # and the triangle has an area of #45 #. What are the lengths of sides A and B?
- An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of #16 # and the triangle has an area of #64 #. What are the lengths of sides A and B?
- An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of #8 # and the triangle has an area of #16 #. What are the lengths of sides A and B?
- Ishmael owns a triangular piece of land. The sides of the land measure 6 mi by 8 mi by 9 mi. Is the land a right triangle?
- A right triangle has sides A, B, and C. Side A is the hypotenuse and side B is also a side of a rectangle. Sides A, C, and the side of the rectangle adjacent to side B have lengths of #12 #, #3 #, and #5 #, respectively. What is the rectangle's area?
- A right triangle has sides A, B, and C. Side A is the hypotenuse and side B is also a side of a rectangle. Sides A, C, and the side of the rectangle adjacent to side B have lengths of #7/9 #, #2/5 #, and #8 #, respectively. What is the rectangle's area?
- A right triangle has two sides that are each 12 feet long. To the nearest foot, what is the length of the third side?
- A right triangle has sides A, B, and C. Side A is the hypotenuse and side B is also a side of a rectangle. Sides A, C, and the side of the rectangle adjacent to side B have lengths of #9 #, #4 #, and #5 #, respectively. What is the rectangle's area?
- A right triangle has sides A, B, and C. Side A is the hypotenuse and side B is also a side of a rectangle. Sides A, C, and the side of the rectangle adjacent to side B have lengths of #7 #, #4 #, and #1 #, respectively. What is the rectangle's area?
- A right triangle has sides A, B, and C. Side A is the hypotenuse and side B is also a side of a rectangle. Sides A, C, and the side of the rectangle adjacent to side B have lengths of #7 #, #2 #, and #9 #, respectively. What is the rectangle's area?
- In an isosceles triangle LMN, LM=39cm, NL=39cm and MN = 27cm, how do you calculate the height of the triangle LMN?
- A rectangular garden is 28 feet long. If you walk diagonally across the garden, you would walk 35 feet. How many feet wide is the garden?
- And I saucily‘s right triangles legs are 10 square root of 8 feet long. What is the length of the hypotenuse?
- The legs of a right triangle are 4 cm and 7 cm long. To the nearest cm, how long is the hypotenuse?