Triangle Area and Pythagorean Theorem

Mr. Collier presents a challenging Pythagorean theorem problem involving a right triangle with a hypotenuse of 14 meters. The longer leg is twice the length of the shorter leg. He guides through drawing the triangle, setting up the equation using the Pythagorean theorem, solving for x, and finally calculating the area of the triangle. The solution involves understanding the relationship between the sides of the triangle and applying the area formula for triangles.

What is the length of the hypotenuse in the given problem?

• 12 M

• 16 M

• 14 M

• 18 M

If the longer leg is twice the shorter leg, how is the longer leg expressed in terms of x?

• x

• 2x

• 3x

• 4x

What is the formula for the Pythagorean theorem?

• a^2 + b = c^2

• a^2 + b^2 = c

• a + b = c^2

• a^2 + b^2 = c^2

What is the equation formed using the Pythagorean theorem for this problem?

• x^2 + 2x^2 = 14^2

• x^2 + 4x^2 = 196

• x^2 + 2x^2 = 196

• x^2 + 4x^2 = 14^2

What is the value of 14 squared?

• 256

• 144

• 196

• 169

After dividing both sides by 5, what is the value of x^2?

• 39.2

• 59.2

• 49.2

• 29.2

What is the most accurate way to express the value of x?

• Square root of 59.2

• Square root of 39.2

• Square root of 29.2

• Square root of 49.2

Why is it important to keep the value of x as the square root of 39.2?

• To simplify calculations

• To avoid using a calculator

• To make it easier to remember

• To ensure accuracy

What is the formula for the area of a triangle?

• Base * Height

• 1/2 * Base * Height

• Base + Height

• 1/2 * Base + Height

What is the base of the triangle in terms of x?

• Square root of 39.2

• 2x

• 2 * Square root of 39.2

• x