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The length of a brace [tex]\([b]\)[/tex] that needs to be replaced under the deck is found by the radical equation [tex]\([b=\sqrt{2 l}]\)[/tex].

Find the length of a brace needed with [tex]\([l=4.5]\)[/tex] feet.

The length of the new brace must be [tex]\(\_\_\_\_\)[/tex] feet.



Answer :

GinnyAnswer
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.

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