# Can someone show me how to set up and solve this problem? If a sqare room has a diagonal measurement of 38 feet, the sides of the room have a lenth of?

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### 2 Answers

Length of diagonal of a square is given by following formula

`d=asqrt2`

where `a` is the length of the side of the square.

`38=asqrt2`

divide both sides by `sqrt2.`

`a=38/sqrt2approx26.870057685`

**Sides of the room have length of `38/sqrt2` feet. **

For this problem, think of the square room as two right triangles. That way, you could use the pythagorean theorem of a^2+b^2=c^2, with c being the length of the diagonal, and a and b the length of the sides.

a^2+b^2=c^2

a^2+b^2=38^2

a^2+b^2=1444

Since the room is a square, both a and b will be equal, so we can just use the variable x to represent the two sides.

x^2+x^2=1444

2(x^2)=1444

x^2=722

x=26.87

The sides of the room have a length of 26.87 feet.