The Play Park runs between Happy Street and Sad Street. Some drivers are using the park as a short cut. A fencing contractor has been asked to put chains across both ends of the park to stop the cars driving through, but he has not been told how wide the park is. When he rang the council, the girl told him the perimeter was 420 metres and the width was 3/4 of the length but she did not know the actual length. What is the length of chain needed for each end of the park?

Question

The Play Park runs between Happy Street and Sad Street. Some drivers are using the park as a short cut. A fencing contractor has been asked to put chains across both ends of the park to stop the cars driving through, but he has not been told how wide the park is. When he rang the council, the girl told him the perimeter was 420 metres and the width was 3/4 of the length but she did not know the actual length. What is the length of chain needed for each end of the park?

Answer 1

length --- x m

width = (3/4)x m

2x + 2(3/4)x = 420
multiply each term by 4 to get rid of fractions
8x + 6x = 1680
14x =1680
x = 120
(3/4)x = 90

The park is 90 m by 120 m

Answer 2

To solve this problem, we need to break it down into steps:

Step 1: Understand the information given.
The perimeter of the park is 420 meters.
The width of the park is 3/4 of the length.

Step 2: Express the width in terms of the length.
Let's assume the length of the park is L meters.
According to the given information, the width of the park is 3/4 of the length, so the width would be (3/4) * L meters.

Step 3: Calculate the perimeter using the length and width.
The perimeter of a rectangle can be calculated using the formula: P = 2(L + W), where P is the perimeter, L is the length, and W is the width.
In this case, the total perimeter is given as 420 meters, so we can set up the equation:
420 = 2(L + (3/4)L)

Step 4: Solve the equation to find the length.
First, simplify the equation:
420 = 2(7/4)L
Divide both sides of the equation by 2:
210 = (7/4)L
Multiply both sides of the equation by 4/7:
L = (210 * 4) / 7
L = 120

Therefore, the length of the park is 120 meters.

Step 5: Calculate the length of chain needed for each end of the park.
As the chains are placed across both ends of the park, we need to find the sum of the width of both ends.
The width of each end is (3/4)L, so the total is: 2 * (3/4)L.

Substituting the value of L from Step 4:
Chain length = 2 * (3/4) * 120
Chain length = 2 * 90
Chain length = 180 meters.

Therefore, 180 meters of chain are needed for each end of the park to effectively block the cars from using it as a shortcut.