ABCD is a square of perimeter 8, If E is the midpoint of AD, what is the altitude from E to CD?

A. 8
B. 6
C. 4
D. 2
E. 1

The OA is E.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.

Hi swerve,
Let's take a look at your question.

The perimeter of square is 8, we know that
Perimeter of square = 4 * Length of a side
Therefore,
8 = 4 * Length of a side
Length of a side = 8/4 = 2

We know that altitude is a perpendicular from a given point to a line. Since E is the midpoint of AD, therefore, an altitude from point E to CD will be ED.
It means we need to find the length of altitude ED.

We know that E is the mid point of AD, therefore ED will be half the length of AD.
$$ED=\frac{1}{2}\left(AD\right)$$
AD is the side of square, therefore,
$$ED=\frac{1}{2}\left(2\right)=1$$

Therefore, Option E is correct.

Hope it helps.
I am available if you'd like any follow up.