A new homeowner buys 120 square feet of carpet for a room in her new house. If the room is square, what is the length of each side of the room? (Recall that the area of a square is calculated by I^2, where l is the length of one side.)

Question

A new homeowner buys 120 square feet of carpet for a room in her new house.  If the room is square, what is the length of each side of the room? (Recall that the area of a square is calculated by I^2, where l is the length of one side.)

diamond12300 · Answer

@amorfide

amorfide · Answer

120feet squared
this means area
we know that the room is square

the area of a square

A=LW
where A is area
L is length
and W is the width

we know that a square has equal side lengths, hence Length and width are the same values
so L=W
this means

$$A=L^{2}$$

we know that the area is 120, so A=120
substitute it in to get
$$120=L^{2}$$

amorfide · Answer

now just solve for L

diamond12300 · Answer

HOW?

amorfide · Answer

if I have $$A^{2}=4$$
If I want A, I would square root both sides
$$A=\sqrt{4}$$

amorfide · Answer

use the same method for your question

diamond12300 · Answer

Is it gonna be 2 square root 10

mathmate · Answer

@diamond12300
A good way to check your answer is to square your answer to see if you get back 120, or nearly 120.