Arectangular patio is 9 ft by 6 ft. when the length and width are increased by the same amount, the area becomes 88 sq ft. ginger is using the zero product property to solve the equation (6 + x)(9 + x) = 88. what do her solutions represent?

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.

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.

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,

On solving the above equation we get,

Find the value of x by using split the middle term method,

Using the split the middle term method we get the two factor,

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,

Hence When the length and width are increased by 2 feet then the area of the given rectangular patio becomes 88 sq ft.

Learn more about the area of the rectangle here;

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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).

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step-by-step explanation: