Question

Given the image below. Find the length of side AD.

image.png

Hint: You may need to use Pythagorean Theorem twice.

Given the image below. Find the length of side AD.

Side AB is 20 cm, side BC is 48 cm, side CD is 39 cm

Hint: You may need to use Pythagorean Theorem twice.

Type your answer...

Answer 1

To find the length of side AD, we'll use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side (the hypotenuse).

Let's break it down step by step.

1. **Identify right triangles**:
- Triangle ABC
- Triangle ACD

2. **Calculate the lengths using Pythagorean Theorem**:

First, we need to find the heights involved in triangle ABC:

- Given:
- AB = 20 cm (height from A to line BC)
- BC = 48 cm (the base)

Now let's find the length of AC.

Using the Pythagorean theorem in triangle ABC:

\[
AC^2 = AB^2 + BC^2
\]

Calculating:

\[
AC^2 = 20^2 + 48^2
\]
\[
AC^2 = 400 + 2304
\]
\[
AC^2 = 2704
\]
\[
AC = \sqrt{2704}
\]
\[
AC = 52 \text{ cm}
\]

Next, we now have AC, and we will use it to find AD in triangle ACD.

- Given:
- AC = 52 cm
- CD = 39 cm

Applying the Pythagorean theorem in triangle ACD:

\[
AD^2 = AC^2 + CD^2
\]

Calculating:

\[
AD^2 = 52^2 + 39^2
\]
\[
AD^2 = 2704 + 1521
\]
\[
AD^2 = 4225
\]
\[
AD = \sqrt{4225}
\]
\[
AD = 65 \text{ cm}
\]

Thus, the length of side AD is **65 cm**.