In a rectangle ABCD , E is the mid -point of AB . If AB= 16 m and AD = 6 m , then find ED .

Options

A. 15 cm
B. 10 cm
C. 12 m
D. 14 m

Answer

To find the length of ED in rectangle ABCD, where E is the midpoint of AB, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Dimensions of the Rectangle:**
- Given that AB = 16 m and AD = 6 m, we can label the rectangle ABCD accordingly.
- Therefore, AB = CD = 16 m and AD = BC = 6 m.

2. **Locate Point E:**
- Since E is the midpoint of AB, we can find AE and EB.
- AE = EB = AB/2 = 16 m / 2 = 8 m.

3. **Draw Triangle AED:**
- We will now consider triangle AED. The lengths we have are:
- AE = 8 m (from step 2)
- AD = 6 m (given)

4. **Apply the Pythagorean Theorem:**
- According to the Pythagorean theorem, in right triangle AED:
\[ AD^2 + AE^2 = ED^2 \]
- Plugging in the values:
\[ 6^2 + 8^2 = ED^2 \]
\[ 36 + 64 = ED^2 \]
\[ 100 = ED^2 \]

5. **Calculate ED:**
- To find ED, take the square root of both sides:
\[ ED = \sqrt{100} = 10 \text{ m} \]

### Final Answer:
ED = 10 m

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