Respuesta :
Answer:
Step-by-step explanation:
Multiply out (6 + x)(9 + x) and set the result (product) = to 88 ft²:
54 + 9x + 6x + x² = 88 ft².
Then 54 + 15x + x² - 88 ft² = 0
Combining the constants, we get x² + 15x - 34 = 0
This factors easily to (x + 17)(x - 2) = 0, with the result that x = 2.
We conclude that if we increase both the 9 ft length and the 6 ft width by 2 ft, the new area will be 88 ft². Note that (9+2)(6+2) = 88.
We discard the x-value -17, as we are ADDING the quantity x to the original measurements (9 by 6 ft) to obtain new measurements (11 by 8 ft).
Area of rectangle is the product of its length and breadth. It is measured in unit squared. When the length and breadth are increased by 2 feet then the area of the given rectangular patio becomes 88 sq ft.
Given-
A rectangular patio is 9 ft by 6 ft.
The length of the rectangular patio is 9 ft.
The breadth of the rectangular patio is 6 ft.
What is the area of a rectangle?
Area of rectangle is the product of its length and breadth. It is measured in unit squared
The equation is given for the problem is,
[tex](6 + x)(9 + x) = 88[/tex]
On solving the above equation we get,
[tex]x^2+6x+9x+54= 88[/tex]
[tex]x^2+15x+54-88=0[/tex]
[tex]x^2+15x-34=0[/tex]
Find the value of x by using split the middle term method,
[tex]x^2+17x-2x-34=0[/tex]
Using the split the middle term method we get the two factor,
[tex](x+17)(x-2)=0[/tex]
Equate the above equation to zero we get the values of the x are -17 and 2.
Taking positive value of x and keeping it into the given equation we get,
[tex](6 + x)(9 + x) = 88[/tex]
[tex](6 + 2)(9 + 2) = 88[/tex]
[tex]8\times 11=88[/tex]
[tex]88=88[/tex]
Hence When the length and width are increased by 2 feet then the area of the given rectangular patio becomes 88 sq ft.
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