Quadrilateral FGHI is a rectangle, FH=16a+14, and GI=8a+86. What is FH?

Question

F
I
H
G
J
FH=

Answer 1

To determine the value of \( FH \), we need to remember that in a rectangle, opposite sides are equal in length. Therefore, since \( FGHI \) is a rectangle, it follows that:

\[ FH = GI \]

From your question, we have:

\[ FH = 16a + 14 \] \[ GI = 8a + 86 \]

Setting these two expressions equal to each other gives us:

\[ 16a + 14 = 8a + 86 \]

Now we'll solve for \( a \):

1. Subtract \( 8a \) from both sides:

\[ 16a - 8a + 14 = 86 \] \[ 8a + 14 = 86 \]

2. Subtract 14 from both sides:

\[ 8a = 86 - 14 \] \[ 8a = 72 \]

3. Divide both sides by 8:

\[ a = \frac{72}{8} = 9 \]

Now, we can substitute \( a = 9 \) back into the expression for \( FH \):

\[ FH = 16a + 14 \] \[ FH = 16(9) + 14 \] \[ FH = 144 + 14 \] \[ FH = 158 \]

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

\[ \boxed{158} \]