Question

A room has and area of 294ft^2. one dimension is 7 ft more than the other. What is the length of the longer side of the room?

Answer 1

Given the information, we have the following:

Therefore, we have the following relationship:

$\begin{gathered} A=b\cdot h \\ \Rightarrow294=x\cdot(x+7) \\ \Rightarrow x^2+7x-294=0 \end{gathered}$

Now, solving for x we get the following values:

$\begin{gathered} x^2+7x-294=0 \\ \Rightarrow(x+21)\cdot(x-14)=0 \\ x=-21 \\ or \\ x=14 \end{gathered}$

Since we cannot have a negative length, we take x=14, therefore:

Finally, the longer side of the room is 21 ft