Mathematics, 29.07.2019 08:30 dinajathomas0407

What will be the perimeter and the area of the rectangle below if it is enlarged using a scale factor of 5.5? a rectangle is shown. the length of the rectangle is labeled as 8 cm, and the width is labeled as 6 cm. perimeter = 50 cm, area = 155.25 cm2 perimeter = 50 cm, area = 1,452 cm2 perimeter = 154 cm, area = 155.25 cm2 perimeter = 154 cm, area = 1,452 cm2

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We know that
scale factor =5.5
the dimensions of the original rectangle are
length is 8 cm, and the width is 6 cm.
original perimeter=2*[8+6]> 28 cm
original area=8*6> 48 cm²

perimeter of the larger rectangle=[scale factor]*original perimeter
perimeter of the larger rectangle=5.5*28> 154 cm

area of the larger rectangle=scale factor²*area original rectangle
area of the larger rectangle=5.5²*48> 1452 cm²

the answer is
perimeter=154 cm
area=1452 cm²

Answer from: youtubeviewer109

perimeter is 154 cm
area is 1452 cm^2
This means that the last option is the correct one

Explanation:
1- getting the new dimensions:
We are given that the scale factor is 5.5
This means that:
new length = old length * scale factor
new width = old width * scale factor
We are given that:
scale factor = 5.5
old length = 8 cm
old width = 6 cm
Therefore:
new length = 8 * 5.5 = 44 cm
new width = 6 * 5.5 = 33 cm

2- getting the perimeter:
perimeter of the rectangle can be calculated as follows:
perimeter = 2(length + width)
We have:
length = 44 cm
width = 33 cm
This means that:
perimeter = 2(44+33)
perimeter = 2(77)
perimeter = 154 cm

3- getting the area:
area of rectangle can be calculated as follows:
area = length * width
We have:
length = 44 cm
width = 33 cm
This means that:
area = 44 * 33
area = 1452 cm^2

Hope this helps :)

Answer from: Quest

The scale factor of what ?

Answer from: Quest

answer: 33 ( approx)

step-by-step explanation:

since, in the linear regression formula, the slope is the a in the equation y = b + ax ( by comparing it with the general equation of line y = mx + c )

where, $a = \frac{\sum y \sum x^2 - \sum x\sum xy}{n\sum x^2 - (\sum x)^2}$

here given table is,

price ($), x : 18 23 25 29 30 33

pairs sold, y : 16 13 10 8 6 2

so, $\sum x = 158$ , $\sum y = 55$ , $\sum xy = 1315$ ,

$\sum x^2 = 4308$ and $\sum y^2 = 629$ ,

thus, slop of the given line is,

$a = \frac{55\times 4308-158\times 1315}{6\times 4308-(158)^2}$

⇒ $a = \frac{29170}{884}$

⇒ $a =32.9977375566$ ≈ 33

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