Triangle Properties and Area Calculations

In this video, Anil Kumar explains how to find the sides of a right triangle when the area and hypotenuse are given. The problem involves a right triangle ABC with a hypotenuse of 10 cm and an area of 25 cm². The video demonstrates setting up equations using the Pythagorean theorem and area formula, solving these equations, and applying the quadratic formula to find the unknown sides. The solution reveals that the triangle is isosceles with both sides measuring 5√2 cm. The video concludes with a verification of the solution and encourages viewers to engage with the content.

What is the given hypotenuse length of the triangle?

• 15 cm

• 8 cm

• 10 cm

• 12 cm

What is the area of the triangle?

• 20 cm²

• 35 cm²

• 25 cm²

• 30 cm²

What are the variables used to represent the sides of the triangle?

• A and B

• P and Q

• M and N

• X and Y

According to the Pythagorean theorem, what is the equation relating X and Y?

• X² - Y² = 100

• X² - Y² = 50

• X² + Y² = 50

• X² + Y² = 100

How is the area of the triangle expressed in terms of X and Y?

• X * Y = 25

• X * Y = 50

• X * Y = 100

• X * Y = 75

What is the expression for X in terms of Y derived from the area equation?

• X = 50 / Y

• X = 75 / Y

• X = 25 / Y

• X = 100 / Y

What type of equation is formed after substituting the expression for X into the Pythagorean theorem?

• Cubic equation

• Exponential equation

• Linear equation

• Quadratic equation

What is the value of Y after solving the quadratic equation?

• 5√2

• 10√2

• 20√2

• 15√2

What is the value of X after finding Y?

• 20√2

• 10√2

• 15√2

• 5√2

What type of triangle is formed based on the side lengths?

• Scalene

• Isosceles

• Equilateral

• Right