Find a polynominal for the perimeter and for the area. The demensions are:
Width:b+3, Length:b
The perimeter is:
The area is:
Do not factor.
Please help.
perimeter = 2 (b+3) + 2 b
= 2 b + 6 + 2 b
= 4 b + 6
area = (b+3)(b)
= b^2 + 3 b
To find the polynomial for the perimeter, we need to add up all the sides of the rectangle.
The width is given as "b+3" and the length is given as "b".
So, the perimeter is the sum of all sides, which is 2 times the width plus 2 times the length.
Perimeter = 2(width) + 2(length)
Substituting the given values:
Perimeter = 2(b+3) + 2(b)
To simplify, distribute the 2:
Perimeter = 2b + 6 + 2b
Combine like terms:
Perimeter = 4b + 6
Therefore, the polynomial for the perimeter is 4b + 6.
To find the polynomial for the area, we need to multiply the width by the length.
Again, the width is given as "b+3" and the length is given as "b".
Area = width * length
Substituting the given values:
Area = (b+3) * b
To simplify, distribute the b:
Area = b^2 + 3b
Therefore, the polynomial for the area is b^2 + 3b.
Please note that factoring is not necessary to find the polynomial expressions for the perimeter and the area.