Question

If EI = 2t + 9 and GI = 9t - 12, find GI in rectangle EFGH.HGIEF

Answer 1

Answer:

15

Explanation:

The Lengths EI and GI are equal; therefore,

$\begin{gathered} EI=GI \\ 2t+9=9t-12 \end{gathered}$

adding 12 to both sides gives

$\begin{gathered} 2t+9+12=9t-12+12 \\ 2t+21=9t \end{gathered}$

subtracting 2t from both sides gives

$2t+21-2t=9t-2t$$21=7t$

Finally, dividing both sides by 7 gives

$\boxed{t=3.}$

With the value of t in hand, we now find the length GI.

$GI=9t-12$

putting in the value of t gives

$GI=9(3)-12$$GI=27-12$$\boxed{GI=15}$

which is our answer!