Question

The length and width of a rectangular patio are (x + 7) feet and (x + 9) feet, respectively. If the area of the patio is 190 square feet, what are the dimensions of the patio?

Answer 1

The dimension of the patio are approximately 12.82 ft × 14.82 ft.

Explanation:

Given:

Length of the patio =
`(x+7) feet`

Width of the patio =
`(x+9)\ feet`

Area of the patio =
`190\ ft^2`

We need to find the dimensions of the patio.

Solution:

Now we know that;

Area of the rectangle is equal to length times width.

framing in equation form we get;

`(x+7)(x+9)=190`

Applying distributive property we get;

`x^2+9x+7x+63=190\\\\x^2+16x+63=190`

Now adding 1 on both side we get;

`x^2+16x+63+1=190+1\\\\x^2+16x+64=191\\\\(x+8)^2=191`

Now taking square root on both side we get;

`√((x+8)^2)=\±√(191)`

`x+8=\±√(191)\\ \\x=-8\±√(191)\\\\x=-8+13.82 \ \ \ \ \ Or \ \ \ \ x=-8-13.82\\\\x=5.82\ \ \ \ \ Or \ \ \ \ \ \ \ x = -21.82`

Now we got two values of x one positive and 1 negative now we know that dimension of the patio cannot be negative; so we will discard negative value and consider positive value.

Length of the patio =
`x+7 = 5.82+7 = 12.82\ ft`

Width of the patio =
`x+9 = 5.82+9 =14.82\ ft`

Hence the dimension of the patio are approximately 12.82 ft × 14.82 ft.