The length of a rectangle is (x+2) inches. The width of the rectangle is (x+1) inches.
Write an equation that can be used to determine the area (A) of the rectangle in terms of x.
What is the value of x if the area of the rectangle is 56 square inches?
(x+1)(x+2) = A
x^2 + 3 x + 2 = A
x^2 + 3 x + 2 = 56
x^2 + 3 x - 54 = 0
(x+9)(x-6) = 0
x = 6
this is very stupid
To find the equation for the area of the rectangle in terms of x, we use the formula for the area of a rectangle which is:
A = length * width
Given that the length of the rectangle is (x+2) inches and the width is (x+1) inches, we substitute the values in the formula:
A = (x+2) * (x+1)
Expanding this equation, we get:
A = x^2 + x + 2x + 2
Combining the like terms, we simplify the equation to:
A = x^2 + 3x + 2
So, the equation for the area (A) of the rectangle in terms of x is A = x^2 + 3x + 2.
To find the value of x if the area of the rectangle is 56 square inches, we substitute A = 56 into the equation:
56 = x^2 + 3x + 2
Rearranging the equation to isolate the quadratic term, we get:
x^2 + 3x + 2 - 56 = 0
Simplifying, we have:
x^2 + 3x - 54 = 0
Now, we need to factorize the quadratic equation. We observe that -6 and 9 are factors of -54, and their sum is 3:
(x - 6)(x + 9) = 0
Setting each factor equal to zero gives us the values of x:
x - 6 = 0 or x + 9 = 0
Solving for x, we find:
x = 6 or x = -9
Therefore, if the area of the rectangle is 56 square inches, the possible values for x are x = 6 or x = -9.