Pythagorean Theorem Worksheets Grade 8

1. A rectangular field has a length of 3.6 × 10³ meters and a width of 4.8 × 10³ meters. A diagonal path is built across the field. Using the Pythagorean theorem, find the length of the diagonal path in scientific notation.
2. A right triangle has legs of length 5 cm and 12 cm. What is the length of the hypotenuse?
3. Liam is building a triangular support brace for his bookshelf. The brace will be a right triangle where the two shorter sides measure 1.2 meters and 1.6 meters. What is the length of the longest side (the hypotenuse) of this triangular brace?

…and 3 more problems

1. Noah is helping his teacher create a visual proof of the Pythagorean theorem for a classroom display. He draws a large square with side length (a + b), where a = 6 cm and b = 1 cm. Inside the large square, Noah places four congruent right triangles, each with legs a and b, arranged so that their hypotenuses form a smaller inner square. Explain how this area model proves that a² + b² = c² for any right triangle, and determine the side length c of the inner square (the hypotenuse).
2. A drone is flying directly from a control station to a delivery point. The drone flies 2.4 kilometers east and then 1.8 kilometers north to reach its destination. What is the straight-line distance, in kilometers, between the control station and the delivery point?
3. Liam is designing a triangular garden with sides measuring 6 meters and 8 meters. He needs to know the length of the diagonal side to purchase enough fencing. What is the length of the diagonal side of his garden?

…and 4 more problems

1. A right triangle has legs measuring 7 cm and 24 cm. Using the Pythagorean theorem, find the length of the hypotenuse in centimeters.
2. A right triangle has legs of length 9 cm and 12 cm. What is the length of the hypotenuse?
3. A right triangle has legs measuring 12 cm and 16 cm. What is the length of the hypotenuse?

…and 6 more problems