Solve by completing the square: a rectangular patio has a length of x+6m, a width of x+8m, and the total area of 400 m^2. find the dimensions to the nearest tenth

Length of the rectangular patio = (x + 6) m

width of the rectangular patio = (x +8)m

Area of rectangle=Length*Width.

400=(x+6)(x+8)

400=+14x+48

For completing square, first add - 48 on both side

400 - 48 = +14x

352 = +14x

To make a complete square add the third term =

a= 1 and b= 14

Third term =

Third term = 49

Now add 49 in both side of the equation

352 + 49 = +14x + 49

401 =

Taking square root on both sides

We can not consider the negative value

so x + 7 = 20.02

x = 20.02 -7

x= 13.02

Length of the rectangular patio = (x + 6) = 13.02 + 6 = 19.02 m

width of the rectangular patio = (x +8) = 13.02 + 8 = 21.02 m