Question

To protect your town from a possible zombie invasion, your city council decides to build a wall. The Waters Proposal suggests building a wall 20 feet tall that the would weigh approximately 43275 tons. A second proposal, the Barrett Proposal, says that 20 feet is too short, and the wall in the Waters Proposal is also not long enough or thick enough to keep out zombies. He suggests scaling up the wall, i.E increasing all the dimensions of the wall by the same percentage. Under this plan, the height of the wall would be 34 feet tall and the new perimeter would be 9809 feet long. What would the perimeter of the wall under the Waters Proposal be? feet.

Answer 1

5770 feet

Explanation:

The height of the wall under the Waters proposal is 20 feet and the height of the wall under the Barrett proposal is 34 feet and its perimeter is 9809 feet. Since there is an increase in the dimensions of the wall, we find this percentage increase.

So, the percentage increase in the height of the wall is thus (New height - Old height)/Old height × 100%

New height = 34 feet and Old height = 20 feet

So, Percentage increase = (New height - Old height)/Old height × 100% = (34 ft - 20 ft)/20 ft × 100 % = 14/20 × 100% = 7/10 × 100% = 70 % increase.

Since all the dimensions increase by the same amount, the perimeter in the Waters proposal increases by 70% to the perimeter in the Barrett proposal.

Let P = perimeter in the Waters proposal and P' = perimeter in the Barrett proposal.

So, the percentage increase in perimeter is

(P' - P)/P × 100 % = 70 %

We now find P

(P' - P)/P = 70%/100%

(P' - P)/P = 0.7

P' - P = 0.7P

P' = 0.7P + P

P' = 1.7P

P = P'/1.7

So, substituting the value for P' = 9809 feet

P = P'/1.7

= 9809 ft/1.7

= 5770 feet

So, the perimeter of the wall under the Waters Proposal is 5770 feet.