Answer:
The dimension of the patio are approximately 12.82 ft × 14.82 ft.
Step-by-step explanation:
Given:
Length of the patio = [tex](x+7) feet[/tex]
Width of the patio = [tex](x+9)\ feet[/tex]
Area of the patio = [tex]190\ ft^2[/tex]
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;
[tex](x+7)(x+9)=190[/tex]
Applying distributive property we get;
[tex]x^2+9x+7x+63=190\\\\x^2+16x+63=190[/tex]
Now adding 1 on both side we get;
[tex]x^2+16x+63+1=190+1\\\\x^2+16x+64=191\\\\(x+8)^2=191[/tex]
Now taking square root on both side we get;
[tex]\sqrt{(x+8)^2}=\±\sqrt{191}[/tex]
[tex]x+8=\±\sqrt{191}\\ \\x=-8\±\sqrt{191}\\\\x=-8+13.82 \ \ \ \ \ Or \ \ \ \ x=-8-13.82\\\\x=5.82\ \ \ \ \ Or \ \ \ \ \ \ \ x = -21.82[/tex]
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 = [tex]x+7 = 5.82+7 = 12.82\ ft[/tex]
Width of the patio = [tex]x+9 = 5.82+9 =14.82\ ft[/tex]
Hence the dimension of the patio are approximately 12.82 ft × 14.82 ft.
