Finding Length DB in a Complex Triangle Configuration: 6-Unit Height Problem

Given the triangles in the drawing

What is the length of the side DB?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find DB
00:03 We'll use the Pythagorean theorem in triangle ABC
00:12 We'll substitute appropriate values and solve for BC
00:22 Isolate BC
00:30 This is the length of side BC
00:33 Now we'll use the Pythagorean theorem in triangle BCD
00:43 We'll substitute appropriate values and solve for BD
00:49 Isolate BD
00:56 And this is the solution to the problem

Step-by-step written solution

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1

Understand the problem

Given the triangles in the drawing

What is the length of the side DB?

666222AAABBBCCCDDD

2

Step-by-step solution

In this question, we will have to use the Pythagorean theorem twice.

A²+B²=C²

Let's start by finding side CB:

6²+CB²=(2√11)²

36+CB²=4*11

CB²=44-36

CB²=8

CB=√8

We will use the exact same way to find side DB:

2²+DB²=(√8)²

4+CB²=8

CB²=8-4

CB²=4

CB=√4=2

3

Final Answer

2 cm

Practice Quiz

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Consider a right-angled triangle, AB = 8 cm and AC = 6 cm.
Calculate the length of side BC.

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