30.8k views
4 votes
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?

User Dikesh
by
4.7k points

1 Answer

1 vote

Answer:

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.

User Ashan
by
4.2k points