Pythagorean Theorem Worksheets - Free Printable

Now I have a clear view of all five problems. Let me solve each one using the Pythagorean Theorem (a² + b² = c²), where c is the hypotenuse (longest side) of a right triangle, and a and b are the other two sides.

Problem 1:
Ruth develops a blueprint with a right triangle. The longest side (hypotenuse) measures 14 inches, and one of the other sides measures 12 inches. We need to find the length of the other side.

Using the Pythagorean Theorem:
a² + b² = c²
Let's say a = 12 inches, c = 14 inches, and we need to find b.
12² + b² = 14²
144 + b² = 196
b² = 196 - 144
b² = 52
b = √52 ≈ 7.21 inches

Problem 2:
Carol bought a coloring book that is 11 inches long and 8 inches wide. We need to find the diagonal length.

The diagonal forms the hypotenuse of a right triangle with sides 11 inches and 8 inches.
a² + b² = c²
11² + 8² = c²
121 + 64 = c²
185 = c²
c = √185 ≈ 13.60 inches

Problem 3:
The slope of the rafter is 15 feet, and half the run of the rafter measures 12 feet. We need to find the height of the ridge from the floor.

This forms a right triangle where the slope (rafter) is the hypotenuse (15 feet), and half the run is one leg (12 feet). We need to find the height (other leg).
a² + b² = c²
Let's say a = 12 feet, c = 15 feet, and we need to find b.
12² + b² = 15²
144 + b² = 225
b² = 225 - 144
b² = 81
b = √81 = 9 feet

Problem 4:
A ramp is attached to a height of 27 inches from the floor. The horizontal distance between the lower end of the ramp and the floor is 60 inches. We need to find the length of the ramp.

The ramp forms the hypotenuse of a right triangle with legs 27 inches and 60 inches.
a² + b² = c²
27² + 60² = c²
729 + 3600 = c²
4329 = c²
c = √4329 ≈ 65.80 inches

Problem 5:
Ashley has a right triangular garden in her backyard. The longest side (hypotenuse) measures 17 yards, and one of the sides is 15 yards long. We need to find the length of the other side.

Using the Pythagorean Theorem:
a² + b² = c²
Let's say a = 15 yards, c = 17 yards, and we need to find b.
15² + b² = 17²
225 + b² = 289
b² = 289 - 225
b² = 64
b = √64 = 8 yards

Here are the solutions to all five problems:

1. The other side of Ruth's instrument measures approximately 7.21 inches.
2. The diagonal length of Carol's coloring book is approximately 13.60 inches.
3. The height of the ridge from the floor is 9 feet.
4. The length of the ramp is approximately 65.80 inches.
5. The length of the other side of Ashley's garden is 8 yards.