Algebra Question

Question

Echo Engineering builds rectangular settling tanks that include covered tops. Rubber stripping must be placed around the edge of the rectangular settling tank to seal the top covering. Seymour Industries contracted a project with Echo Engineering to construct two settling tanks, including the rubber stripping. Since Tank A is to be larger than Tank B, Tank A will require more rubber stripping than Tank B. 

Tank A will have a length in feet represented by 25x + 12 and a width in feet represented by 7x + 18. Write and simplify an expression that could be used to determine the amount of rubber stripping, in feet, needed to place around the top edge of this rectangular settling tank.

Answer 1

The rubber stripping must go all the way around the top edge of the rectangular tank. Since the tank is a rectangle, we need to find its perimeter.

The formula for the perimeter of a rectangle is:

P = 2L + 2W

where L represents the length and W represents the width.

The length of Tank A is:

25x + 12

The width of Tank A is:

7x + 18

Lets substitute these expressions into the perimeter formula and simplify:

P = 2(25x + 12) + 2(7x + 18)

= 50x + 24 + 14x + 36

= 64x + 60

This means that Tank A will require 64x + 60 feet of rubber stripping to seal the top edge.

Answer 2

Hi Salem Y

Tank A length around the top sounds like the Perimeter of the top face only, since the height is not involved here, of your rectangular tank

L= 25x + 12,

W = 7x + 18

P = 2(L) + 2(W)

Just plug in the equations given for L and W, multiply and combine like terms

Give it a try

Tank B

According to your comment, gives the width, W and area A, of the top face again since the height is not involved

Area = LW = 360x + 495

W = 8x + 11

L(8x + 11) = 360x + 495

L = (360 + 495)/(8x + 11)

Long division

L = 45

Check it

45(8x + 11) = 360x + 495

Answer 3