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2 years ago

7

the largest of these five squares has side length 27 units, and each additional square's side length is 2/3 as large as the one

before. What is the perimeter and area of the entire shape?

1 answer:

RoseWind [281]2 years ago

4 0

The total area is 1289.41 units².

The total perimeter is 281.32 units.

<h3>What is the total area and perimeter?</h3>

The first step is to determine the side lengths of the other squares:

Length of the second square = 2/3 x 27 = 18
Length of the third square = 2/3 x18 = 12
Length of the fourth square = 2/3 x 12 = 8
Length of the fifth square = 2/3 x 8 = 5.33

Area of a square = length²

Perimeter of a square = 4 x length

Area of the first square = 27² = 729
Area of the second square = 18² = 324
Area of the first square = 12² = 144
Area of the first square = 8² = 64
Area of the first square = 5.33² = 28.41

Total area = sum of the areas of the 5 squares = 1289.41 units²

Perimeter of the first square = 4 x 27 = 108 units
Perimeter of the second square = 4 x 18 = 72
Perimeter of the third square = 4 x 12 = 48
Perimeter of the fourth square = 4 x 8 = 32
Perimeter of the fifth square = 4 x 5.33 = 21.32

Total perimeter = 281.32 units

To learn how a square, please check: brainly.com/question/9030544

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2 years ago

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1 year ago

Brainliest to correct answer

Gnesinka [82]

Question 1:

For this case we must factor the following expression:

$n ^ 2 + 2n-24 = 0$

We must find two numbers that when multiplied result in -24 and when added together result in 2. These numbers are: 6 and -4.

$6*(-4)=-24\\6-4=2$

Thus, we factor:

$(x + 6) (x-4) = 0$

The roots are:

$x_ {1} = - 6\\x_ {2} = 4$

Answer:

Option C

Question 2:

For this case we have that by definition, the area of a rectangle is given by:

$A = w * l$

Where:

w: Is the width of the rectangle

l: is the length of the rectangle

According to the statement we have:

$A = 30 \ ft ^ 2\\l = 3w-1$

Substituting:

$(3w-1) w = 30\\3w ^ 2-w = 30\\3w ^ 2-w-30 = 0$

Where:

$a = 3\\b = -1\\c = -30$

The solution:

$x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}\\x = \frac {- (- 1) \pm \sqrt {(- 1) ^ 2-4 (3) (- 30)}} {2 (3)}\\x = \frac {1 \pm \sqrt {1 + 360}} {2 (3)}\\x = \frac {1 \pm \sqrt {361}} {6}\\x = \frac {1\pm19} {6}\\$

We have two roots:

$x_ {1} = \frac {1-19} {6} = \frac {-18} {6} = - 3\\x_ {2} = \frac {1 + 19} {6} =\frac {20} {6} = 3,333$

We choose the second value (the positive), when rounding is $3.33 \ ft$

Answer:

Option A

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