Question

help fan +medal

The sides of a square are increased by a scale factor of 7. The perimeter of the smaller square is 16 ft. What is the perimeter of the larger square?

Answer 1

Hi,

Do you know what a perimeter is ?

Answer 2

A perimeter is the continuous line forming the boundary of a closed geometric figure.

Answer 3

Yep. It can be viewed as the sum of the length of each of the sides of a geometric figure.

Answer 4

In a square, the 4 sides are equal. It means that if one side has length \(x\) ft, then there will be 4 sides with length of \(x\).

Answer 5

So, 4 ft?

Answer 6

Nope. It will be:

\(\large{x + x +x +x = perimeter}\)

Answer 7

You're told that the perimeter is 16ft. And so:

\(\large{x + x +x +x = 16}\)

\(\large{4x = 16}\)

Answer 8

My answer choices are:

4 ft.
28 ft.
56 ft.
112 ft.

Answer 9

Excellent.

If you solve for x, you'll have the length of one side. And you're told that each side was stretched by a factor of 7. 'By a factor of something' means that each sides was multiplied by that something.

Answer 10

Do you guess what would be the next step then?

Answer 11

No.

Answer 12

Is it 28 ft?

Answer 13

Let find the length of one side.

\(\large{4x = 16}\)

\(\large{x = \frac{16}{4}}=4\)

Answer 14

4 was stretched by a factor of 7, which is:

\(\large{4*7 = 28}\)

Answer 15

Was I right?

Answer 16

Your new square looks like this:

Answer 17

Okay, so, I was right.

Answer 18

Yep. BUT 28ft is just one side. And the perimeter is the sum of all sides of the square.

Answer 19

You need to sum four 28's.

Answer 20

Or:

\(4* 28\)

Answer 21

So the perimeter is 112. So what is the answer 28 or 112???

Answer 22

Since the perimeter is the sum of all sides. The answer is \(4* 28= 112\)ft.