Question

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

\[
\boxed{158}
\]