1. Vince wants to make a square patio in his yard. He has enough concrete to pave an area of 378 square feet. How long can a side of his patio be

Length of the side is:

x = 19.44 ft

Step-by-step explanation:

Shape of the patio = Square

Area of patio = 378 ft²

We know that for square, all the sides are equal to each other and all the angles are equal to each other.

Let the side of the square = x

We need to find x

We know that for square.

Area of square = Length * Width

As all sides are equal, length is equals to x and width is also equals to x.

Where Area is equals to 378 ft²

Substitute values:

378 ft² = x*x

x² = 378 ft²

Taken square root on both sides

√x² = √378 ft²

x = 19.44 ft, x = - 19.44 ft

As the length cannot be a negative value

x = 19.44 ft

The length of a side can be 3·√42 ft long

Step-by-step explanation:

The question is a word problem regarding the formula for the area of a square

The parameters given are;

Available concrete = Enough to pave 378 ft.²

Shape of patio Vince wants to make = Square

Therefore, the dimensions of the sides, s, of a square patio that has an area of 378 ft.² is found as follows;

s² = 378

Therefore, s = √378 = √ (9 * 42) = 3·√42 ft

Hence, the length of a side can be 3·√42 ft long.