Answer:
1a) length = 4.5x - 18, or 3.5x - 14. width = 2x-2 (make sure you write the expression)
b) perimeter = 13x-40 (make sure you write the expression)
c) x = 14
Step-by-step explanation:
1a) to find the length, we need to add all the terms that make up the length. the terms are 2x-10 , x-2 , 1/2x-4 , and x-2
now let's add the terms
2x - 10 + x - 2 + 0.5x - 4 + x - 2 = 4.5x - 18
you can also find the length of the other opposite side, but it will equal the same thing we just got so it isn't necessary, but it's 3.5x - 4 (do the same thing we did previously)
the width is made up of two terms, x - 2 and x.
now let's add the two terms
x - 2 + x = 2x - 2
1b)
the perimeter of a rectangle is twice the width plus twice the length
P rectangle = 2L + 2W
so we substitute our answers from 1a
P rectangle = 2(4.5x-18) + 2(2x-2) . remember you are multiplying the entire expression by 2! which is why we need parenthesis.
simplify the equation to get P rectangle = 13x - 40
remember to write the answer as just 13x-40, since it's an expression
1c)
we use 13x-40 from 1b to answer this
142ft = 13x - 40
x = 14
extra:
you can find x just by knowing the lengths. since the lengths are 4.5x - 18 and 3.5x -4, just set them equal to find x, because lengths of a rectangle are equal
4.5x - 18 = 3.5x -4
x = 14
