Maria makes a quilt. The main design is 5 feet long on each side. Then she adds a border around the main design. The finished quilt has an area of 36 square feet.

1. What is the length of one side of the finished quilt?

2. By how much does the border increase the total length of each side of the quilt?

3. The border goes around the whole quilt. What is the width of the border? Explain how you found your answer.

1) The length of one side of the finished quilt is; 6 ft

2) The increase in the total length of each side of the quilt is; 1 ft

3) The width of the border round the quilt is; 0.5 ft

We are told that the main design has each side to be 5 ft long.

Now, she adds a border all round and as a result the area of the quilt is now 36 ft²

A) Since the quilt is a square and the area is 36 ft², we know that;

Area of a square = s²

Where s is length of one side.

Thus;

s² = 36

s = √36

s = 6 ft

B) Since the initial length of a side was 5 ft and the new length is 6 ft, then the difference is;

6 - 5 = 1 ft

Thus, the border made each side length of the quilt increase by 1 ft.

C) Since the border goes all round, since the difference in length is 1 ft, it means that the width of each border is; ½ ft = 0.5 ft

Read more about area of a square at; link

1. 6 feet

2. 1 ft

0.5 ft

Step-by-step explanation:

The given dimensions for the quilt are;

The length of each sides of the quilt = 5 feet long, therefore, the shape of the quilt is a square

The area, A, of the finished quilt plus the border = 36 ft²

1. Given that the quilt's shape is that of a square, we have;

A = (side length)²

Side length = √A = √36 = 6 feet

2. Given that the initial length of the sides of the quilt are 5 feet, we have;

Increase in total length by border = Final length of quilt - Initial length of quilt

Increase in total length by border = 6 ft - 5 ft = 1 ft

The increase in total length of the quilt by the border = 1 ft

3) Given that the increase in the length by the border = 1 ft

The sum of the width of the border on both sides = 1 ft

Border width on one side + Border width on the other side = 1 ft

Since there is equal border width on each side of the quilt, we have;

2 × Border width = 1 ft

Border width = width of the border = 1 ft/2 = 0.5 ft.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for