Finding the Median Length BD in a Right Triangle with AC = 10

Median to Hypotenuse with Right Triangle

ABC is a Right triangle

Since BD is the median

and given that AC=10.

Find the length of the side BD.

AAABBBCCCDDD10

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Determine the length of BD
00:03 The following is the size of hypotenuse according to the given data
00:06 BD is the median according to the given data
00:10 The triangle is right-angled according to the given data
00:16 The median to the hypotenuse in a right triangle equals half the hypotenuse
00:24 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

ABC is a Right triangle

Since BD is the median

and given that AC=10.

Find the length of the side BD.

AAABBBCCCDDD10

2

Step-by-step solution

We can calculate BD according to the following rule:

In a right triangle, the midpoint of the hypotenuse is equal to half of the hypotenuse.

That is:

BD is equal to half of AC:

Given that: AC=10 AC=10

BD=10:2=5 BD=10:2=5

3

Final Answer

5

Key Points to Remember

Essential concepts to master this topic
  • Rule: In a right triangle, median to hypotenuse equals half hypotenuse
  • Technique: Since AC = 10, then BD = AC ÷ 2 = 5
  • Check: BD should equal distance from B to midpoint D of AC ✓

Common Mistakes

Avoid these frequent errors
  • Using wrong triangle side as hypotenuse
    Don't assume AC is the hypotenuse just because it's given = wrong calculation! The hypotenuse is always opposite the right angle. Always identify which angle is 90° first, then find the opposite side.

Practice Quiz

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Is the straight line in the figure the height of the triangle?

FAQ

Everything you need to know about this question

How do I know which side is the hypotenuse?

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The hypotenuse is always the longest side and sits opposite the right angle (90°). Look for the small square symbol in the diagram to find the right angle!

Why is the median to the hypotenuse exactly half its length?

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This is a special property of right triangles! When you draw a median from the right angle to the hypotenuse, it creates an isosceles triangle where the median equals the two equal sides.

What if I don't know which angle is the right angle?

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Look for these clues in the diagram: a small square symbol at the vertex, or two sides that appear perpendicular (form an L-shape). The problem states it's a right triangle, so one angle must be 90°.

Can I use the Pythagorean theorem instead?

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You could, but you'd need to know the lengths of both legs first. The median rule is much faster: BD=AC2 BD = \frac{AC}{2} gives you the answer directly!

Does this rule work for all triangles?

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No! This special property only works for right triangles. In other triangles, the median to any side has a different formula involving all three sides.

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