To find the length of the new brace, we start with the given radical equation:
[tex]\[ b = \sqrt{2l} \][/tex]
Where:
- [tex]\( b \)[/tex] is the length of the brace
- [tex]\( l \)[/tex] is the given length under the deck
We are provided with [tex]\( l = 4.5 \)[/tex] feet. We will substitute this value into the equation to find [tex]\( b \)[/tex].
First, substitute [tex]\( l = 4.5 \)[/tex] into the equation:
[tex]\[ b = \sqrt{2 \times 4.5} \][/tex]
Now, perform the multiplication inside the square root:
[tex]\[ b = \sqrt{9} \][/tex]
The square root of 9 is 3:
[tex]\[ b = 3 \][/tex]
Therefore, the length of the new brace needed is 3 feet.
The length of the new brace must be 3 feet.
