Question

0 As shown in the diagram below, M, R, and T are

midpoints of the sides of ABC.
If AB = 18, AC = 14, and BC = 10, what is the
perimeter of quadrilateral ACRM?
1) 35
2) 32
24
4) 21​

Answer 1

The answer to your question is A.35

Answer 2

The perimeter of quadrilateral ACRM is 30. The closest option is 32 (Option 2).

Since M, R, and T are midpoints of the sides of ABC, they divide each side into two equal parts. Therefore, AM = MB, BR = RC, and CT = TA.

Now, let's find the lengths of AM, BR, and CT.

1. **Length of AM:**

`\[ AM = (1)/(2) \cdot AB = (1)/(2) \cdot 18 = 9 \]`

2. **Length of BR:**

`\[ BR = (1)/(2) \cdot BC = (1)/(2) \cdot 10 = 5 \]`

3. **Length of CT:**

`\[ CT = (1)/(2) \cdot AC = (1)/(2) \cdot 14 = 7 \]`

Now, we need to find the perimeter of quadrilateral ACRM:

`\[ \text{Perimeter} = AM + BR + RC + CT \]`

`\[ \text{Perimeter} = 9 + 5 + 7 + 9 = 30 \]`

So, the perimeter of quadrilateral ACRM is 30. The closest option is 32 (Option 2). Please double-check the answer choices, as the calculated perimeter is not exactly matching any of the provided options.