Question

The scalene triangle below, ∆ABC, has side lengths a, b, and c centimeters. Let A' be the image of A when the triangle is reflected across BC. Which of the following is an expression for the perimeter, in centimeters, of the quadrilateral A'BAC ?

Question 3 options:

2(a + b) + c


2(a + c)


2(b + c)


2(a + b + c)


2(a + b)

Answer 1

2(b+c) is the answer

Explanation:

Answer 2

Answer: 2(a + b) + c.

Explanation:

To find the expression for the perimeter of the quadrilateral A'BAC, we need to consider the lengths of the sides involved.

In the given triangle ∆ABC, A' is the image of A when the triangle is reflected across BC. This means that the side BC remains the same in the quadrilateral A'BAC.

The perimeter of a quadrilateral is the sum of all its side lengths. In this case, the quadrilateral A'BAC has three sides that we need to consider: AB, A'B, and AC.

The length of side AB is the same as side A'B in the quadrilateral, and the length of side AC remains the same.

Therefore, the expression for the perimeter of the quadrilateral A'BAC would be:

AB + A'B + AC

Since AB + A'B is equivalent to 2(a + b) (twice the sum of side lengths AB and BC), and AC is equivalent to c, the correct expression for the perimeter is:

2(a + b) + c

Therefore, the correct option is: 2(a + b) + c.