Understanding the Pythagorean Theorem and Its Applications

This video tutorial covers the Pythagorean theorem, explaining its formula and application in solving geometric problems. It includes examples of calculating the hypotenuse and a leg of right triangles, as well as word problems involving the perimeter of a rhombus and the area of an isosceles trapezoid.

What is the formula for the Pythagorean theorem?

• a^2 + b^2 = c^2

• a^2 - b^2 = c^2

• a^2 + b^2 = 2c^2

• a^2 = b^2 + c^2

In a right triangle, if one leg is 5 and the other is 12, what is the length of the hypotenuse?

• 17

• 10

• 13

• 15

If the hypotenuse of a right triangle is 10 and one leg is 5, what is the length of the other leg?

• √50

• √75

• 7

• 5

How can the square root of 75 be simplified?

• 5√3

• 3√5

• 15

• 25

What is the area of a square with a diagonal of 12 inches?

• 144 square inches

• 72 square inches

• 36 square inches

• 24 square inches

In a rhombus, if one diagonal is 14 and the other is 48, what is the perimeter?

• 112

• 100

• 96

• 104

What is the length of each side of a rhombus if its diagonals are 14 and 48?

• 26

• 24

• 25

• 28

What is the formula for the area of an isosceles trapezoid?

• 1/2 (b1 - b2) * h

• b1 * b2 * h

• 1/2 (b1 + b2) * h

• b1 + b2 + h

If the bases of an isosceles trapezoid are 12 and 20, and the height is 3, what is the area?

• 60

• 36

• 48

• 72

In an isosceles trapezoid, if the height is 3 and the bases are 12 and 20, what is the length of the non-parallel sides?

• 5

• 4

• 6

• 7