Quadrilateral EFGH is a rectangle, GI=b+54, and HI=19b. What is the value of b?

Question

G
H
E
F
I
b=

Answer 1

To find the value of \( b \) in the rectangle \( EFGH \), we need to establish the relationships from the geometry of the rectangle.

Given that:

• \( GI = b + 54 \)
• \( HI = 19b \)

In a rectangle, the opposite sides are equal. Thus:

1. \( GI \) is a side of the rectangle.
2. \( HI \) is the adjacent side of the rectangle.

In the context of a rectangle, since both are lengths, we can equate the values of \( GI \) and \( HI \) under the conditions that they are the sides of the rectangle:

\[ b + 54 = 19b \]

Now, solve this equation for \( b \):

1. Subtract \( b \) from both sides: \[ 54 = 19b - b \] \[ 54 = 18b \]

2. Now divide both sides by 18: \[ b = \frac{54}{18} \] \[ b = 3 \]

Thus, the value of \( b \) is:

\[ \boxed{3} \]