ON THE SMARTBOARD, THE
MATH TEACHER DREW A
RECTANGLE WITH A PERIMETER
OF 406 cm. THE LENGTH OF THE
RECTANGLE IS 7cm LONGER
THAN THE WIDTH. FIND THE
DIMENSIONS OF THE RECTANGLE.
Help me with this please

answer

width = 98 cm

length = 105 cm

set up equations

the perimeter of a rectangle = 2W + 2L

p = 2W + 2L

the perimeter is also 406

406 = 2W + 2L

we know that the length of the rectangle is 7 cm longer than the width so

L = W + 7

substitute equations and solve for width

plug L into p = 2W + 2L to get

406 = 2W + 2(W + 7) distribute the 2 to the terms in the parentheses

406 = 2W + 2W + 14

406 = 4W + 14

392 = 4W

W = 98

substitute equations and solve for length

now that we know the width, we can substitute W in L = W + 7 to find length

L = W + 7

L = 98 + 7

L = 105

final dimensions

width = 98 cm

length = 105 cm

yes because there is exactly one y value for every x value

for function there can't be more than one value for every x value