Quadrilateral DEFG is a square. What is DE?

Question

2y
y+7
E
D
G
F
DE=

Answer 1

To find the length of side \( DE \) in square \( DEFG \), we use the information given for \( DE \). If \( DE = 2y \) and also you mention that \( DE = y + 7 \), we can set up an equation since all sides of a square are equal.

So we can set \( 2y = y + 7 \).

Now, let's solve for \( y \):

1. Subtract \( y \) from both sides: \[ 2y - y = 7 \] \[ y = 7 \]

2. Now we can find the length of \( DE \) by substituting \( y \) back into one of the expressions for \( DE \). We can use either \( 2y \) or \( y + 7 \). Let's use \( DE = 2y \): \[ DE = 2(7) = 14 \]

Thus, the length of \( DE \) is \( 14 \).

So, \( DE = 14 \).