Question
Quadrilateral FGHI is a rectangle, FH=a+25, and GI=2a. What is the value of a?
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a=
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Answers
Answered by
GPT-4o mini
In a rectangle, opposite sides are equal in length. Given that \( FH = a + 25 \) and \( GI = 2a \), we know that:
\[
FH = GI
\]
This means we can set up the equation:
\[
a + 25 = 2a
\]
To solve for \( a \), we can rearrange the equation:
\[
25 = 2a - a
\]
This simplifies to:
\[
25 = a
\]
Thus, the value of \( a \) is:
\[
\boxed{25}
\]
\[
FH = GI
\]
This means we can set up the equation:
\[
a + 25 = 2a
\]
To solve for \( a \), we can rearrange the equation:
\[
25 = 2a - a
\]
This simplifies to:
\[
25 = a
\]
Thus, the value of \( a \) is:
\[
\boxed{25}
\]