Question

The area of this rectangle is 54 square inches. Create an equation to find the value of n. Length is 3(n-1) and the width is n+2

Answer 1

Value of n is 4

The area of a rectangle is equal to the product of its length and width.

we know ,

the area of  rectangle, multiply the length, , and the width, ,

and set the product equal to the area.

area of rectangle        = length * width

            54                  = 3(n - 1) * (n + 2)

             54                 =( 3n - 3) * (n + 2)

multiply ( 3n - 3) with  (n + 2)

we get,

              54                = $3n^{2} + 6n - 3n -6$

              54                = $3n^{2} + 3n -6$

              54                = 3($n^{2} + n -2$)

             $\frac{54}{3}$                  =  ($n^{2} + n -2$)

             18                 =  ($n^{2} + n - 2$)

 $n^{2} + n - 2$ - 18           = 0

 $n^{2} + n - 20$                = 0

solve them

 $n^{2} + 5n + 4n -20$       = 0

 n (n + 5) - 4 (n + 5)   = 0

(n + 5)(n -4)  

then we get,            

n = -5 , n = 4

value of n should not be negative . so value of n is 4

Area of rectangle is the region occupied by a rectangle within its four sides or boundaries.

The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides. Hence, we can say, the region enclosed by the perimeter of the rectangle is its area

Area of rectangle = Length x Breadth

A = lb

how to Factoring Quadratic Equation

Step 1: Consider the quadratic equation ax2 + b x + c = 0

Step 2: Now, find two numbers such that their product is equal to ac and sum equals to b.

(number 1)(number 2) = ac

(number 1) + (number 2) = b

Step 3: Substitute these two numbers in the formula given below:

(1/a) [a x + (number 1)]  [a x + (number 2)] = 0

Step 4: Finally simplify the above equation.

learn more about area of rectangle here :brainly.com/question/35108030

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