Triangle missing side example

TL;DR

Find the missing side of a triangle with a given area using the formula for the area of a triangle.

Transcript

• [Instructor] The triangle shown below has an area of 75 square units. Find the missing side. So pause the video and see if you can find the length of this missing side. Alright, now let's work through this together. They give us the area, they give us this side, right over here, this 11, they give us this length 10, which if we rotate this triang... Read More

Key Insights

• 🔺 The missing side length of a triangle can be found using the formula for the area of a triangle.
• 🎟️ By rotating the triangle, the relationship between the given measurements and the missing side becomes clearer.
• 🙃 Dividing both sides of an equation by the same value is necessary to isolate the variable and find its value.

Questions & Answers

Q: How is the missing side length of the triangle determined?

The missing side length can be determined by using the formula for the area of a triangle, with the known area and the given side length and height. By rearranging the equation, x can be isolated and solved for.

Q: Why is the given side length rotated to be the base of the triangle?

By rotating the triangle and considering the given side as the base, it becomes more apparent that the height of the triangle is equal to 10. This simplifies the equation for the area and allows for the determination of the missing side length.

Q: Why is the given side length of 10 not used in the calculation?

The given side length of 10 is not used in the calculation because it represents the height of the triangle when the given side is considered as the base. The side length of 11 is the relevant measurement for calculating the missing side length.

Q: What is the significance of dividing both sides of the equation by 5?

Dividing both sides of the equation by 5 is necessary to isolate the variable x. This operation ensures that the equation remains balanced, allowing for the solution to be found by dividing 75 by 5, resulting in x = 15.

Summary & Key Takeaways

• The video presents a triangle with a known area of 75 square units and a given side length of 11.

• By rotating the triangle and considering the given side as the base and 10 as the height, the missing side length, x, can be determined.

• Using the formula for the area of a triangle, the equation 75 = 1/2 * x * 10 is derived, leading to x = 15.