Question

Need help with 6 and 8

Answer 1

6.

Given

• 5x-27 = 2x-6

Find

• The side length of a regular pentagon whose side lengths in inches are represented by these values

Solution

Add 27 to get

... 5x = 2x + 21

... 3x = 21 . . . . . . . subtract 2x

... x = 7 . . . . . . . . . divide by 3

Then we can find the expression values to be

... 5x -27 = 2x -6 = 5·7 -27 = 2·7 -6 = 8

The side of the pentagon is 8 inches.

8.

Given

• a rectangle's width is 17 inches
• that rectangle's perimeter is  102 inches

Find

• the length of the rectangle

Solution

Where P, L, and W represent the perimeter, length, and width of a rectangle, respectively, the relation between them is ...

.... P = 2(L+W)

We can divide by 2 and subtract W to find L

... P/2 = L +W

... P/2 -W = L

And we can fill in the given values for perimeter and width ...

... 102/2 -17 = L = 34

The length of the rectangle is 34 inches.