# Video: Applying the Pythagorean Theorem to Solve Problems

π΄π΅πΆπ· is a trapezoid-shaped piece of land where the line segment π΄π· is parallel to the line segment π΅πΆ and the line segment π΄π΅ β₯ the line segment π΅πΆ. Find the length of the line segment π΄π΅ given π΄π· = 24 m, π΅πΆ = 48 m, and π·πΆ = 30 m. Give the answer to the nearest meter.

03:06

### Video Transcript

π΄π΅πΆπ· is a trapezoid-shaped piece of land where the line segment π΄π· is parallel to the line segment π΅πΆ and the line segment π΄π΅ is perpendicular to the line segment π΅πΆ. Find the length of the line segment π΄π΅ given π΄π· is equal to 24 meters, π΅πΆ is equal to 48 meters, and π·πΆ is equal to 30 meters. Give the answer to the nearest meter.

We are told in the question that the line segments π΄π· and π΅πΆ are parallel. We want to calculate the length of π΄π΅, which is perpendicular to both π΄π· and π΅πΆ. We will let this length be equal to π₯ meters. Next, we can draw a line from the point π· to the line segment π΅πΆ. We will let the point of intersection of these two lines be point πΈ. We draw this line π·πΈ such that it is perpendicular to the line π΅πΆ. This creates a right triangle π·πΈπΆ, where the length of π·πΈ will be equal to the length of π΄π΅.

The hypotenuse of our right triangle is equal to 30 meters, and we see that one of the shorter sides π·πΈ is equal to π₯ meters. We can calculate the length of πΈπΆ by subtracting 24 meters from 48 meters. This gives us an answer of 24 meters. In any right triangle, we can calculate the length of a missing side using the Pythagorean theorem. This states that π squared plus π squared is equal to π squared, where π is the length of the longest side or hypotenuse.

Substituting in our values, we have π₯ squared plus 24 squared is equal to 30 squared. 24 squared is equal to 576 and 30 squared is equal to 900. We can then subtract 576 from both sides of this equation, giving us π₯ squared is equal to 324. We can then square root both sides of this equation. As 18 squared is equal to 324 and π₯ must be positive, we know that π₯ is equal to 18.

The length of π΄π΅ must therefore be equal to 18 meters. In this question, we do not need to do any rounding to give our answer to the nearest meter. The length of π΄π΅ is exactly 18 meters.