The length of a rectangular sign is 5 times its width . If the sign's perimeter is 36 inches, what is the signs area in square inches

The area is 45 square inches.

Step-by-step explanation:

so if we know that the the length is 5 times the width then we could represent the length as  5x   and x for the width.  

And we  know the perimeter of the sign so we could set up equation to solve for the side lengths.

The perimeter of a rectangle is  2l + 2w  which means 2 times the length plus two times the width.

2(5x) + 2(x) = 36

10x + 2x = 36

12x = 36

x = 3

Now we know the value of x  so we will plot it into the length and with to find the actually side lengths.

length= 5(3) = 15

width=  3  

Check:  15 + 15 + 3 + 3 = 36  

Now we know the side lengths so to find the area we will have to multiply the length times the width.

3 * 15 = 45  

f

step-by-step explanation:

f

2 equivalent expressions to represent the area of a rectangle and the top is n-3 and the side is 2

area of the rectangle = length * width

given length = n - 3

width = 2

replace it in the area

so area of the rectangle = (n-3) *2

= 2(n-3)

one of the expression is 2(n-3)

to get another expression we distribute 2 inside the parenthesis

2(n-3) is 2n - 6

so another expression is 2n - 6

two equivalent expression are

2(n - 3)   , 2n - 6