How long is the line from B down to AC?
A hard-level "Length" problem.Write the same area two ways — with two different base-and-height pairs — and set them equal. It is the strongest move available when a length cannot be measured directly.
GivenAngle B is a right angle. AB = 6 cm, BC = 8 cm, AC = 10 cm
Hints
- Leave the "?" for later and find the area first. Angle B is a right angle, so AB and BC are already the base and the height.
- 8 × 6 ÷ 2 = 24 cm². That is the area of this triangle.
- Here is the key move: any side may be used as the base. This time let's take the slanted side AC = 10 cm.
- With AC as the base, the perpendicular "?" is exactly the height. So "?" was the height all along.
- Changing which side is the base does not change the triangle, so the area is the same. That gives 10 × ? ÷ 2 = 24.
- Now just undo the formula: ? = 24 × 2 ÷ 10.
Answer 4.8cm
More "Length" problems
- a + b + c = ?
- What is the side of the square?
- How long is MN?
- How long is the rope?
- How long is the pole's shadow?
- How deep was the water?