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Natali [406]
3 years ago
13

I’m a given rectangle the shorter side is 2 units less than the longer side. If we let the longer side be represented as the var

iable x create an expression that represents the perimeter of the rectangle.
Mathematics
1 answer:
jarptica [38.1K]3 years ago
7 0

Answer:

4(x-1)units

Step-by-step explanation:

In a given rectangle, the length of the rectangle is the shorter side while its breadth is the longer side.

Since we have 2 lengths and 2 breadths in a rectangle, the perimeter of the rectangle will be 2L+2x where

L is the length(shorter side) and x is the breadth (longer side).

According to the question, the shorter side(L) is 2 units less than the longer side(x). Mathematically,

L = x-2

Substituting L = x-2 into the formula of perimeter of a rectangle we have,

P = 2(x-2) + 2x

P = 2x-4+2x

P = 4x-4

P = 4(x-1)

The perimeter of the rectangle will be 4(x-1)units

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Answer:

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4 0
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Read 2 more answers
1: In order to solve the inequality -1/4 x > 8, which of the following steps must be done?
pogonyaev

Answer:

Step-by-step explanation:

-1/4x>8

x>8/(-1/4)

x>(8/1)(-4/1)

x>-32/1

x>-32

x<-32

The answer is D.

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-3t+7>=9

-3t>=9-7

-3t>=2

t>=2/-3

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3 0
3 years ago
The top and bottom margins of a poster 66 cm each, and the side margins are 44 cm each. If the area of the printed material on t
jasenka [17]

Answer:

  • width: 24 cm
  • height: 36 cm

Step-by-step explanation:

When margins are involved, the smallest area will be the one that has its dimensions in the same proportion as the margins. If x is the "multiplier", the dimensions of the printed area are ...

  (4x)(6x) = 384 cm^2

  x^2 = 16 cm^2 . . . . . divide by 24

  x = 4 cm

The printed area is 4x by 6x, so is 16 cm by 24 cm. With the margins added, the smallest poster will be ...

  24 cm by 36 cm

_____

<em>Comment on margins</em>

It should be obvious that if both side margins are 4 cm, then the width of the poster is 8 cm more than the printed width. Similarly, the 6 cm top and bottom margins make the height of the poster 12 cm more than the height of the printed area.

_____

<em>Alternate solution</em>

Let w represent the width of the printed area. Then the printed height is 384/w, and the total poster area is ...

  A = (w+8)(384/w +12) = 384 +12w +3072/w +96

Differentiating with respect to w gives ...

  A' = 12 -3072/w^2

Setting this to zero and solving for w gives ...

  w = √(3072/12) = 16 . . . . matches above solution.

__

<em>Generic solution</em>

If we let s and t represent the side and top margins, and we use "a" for the printed area, then the above equation becomes the symbolic equation ...

  A = (w +s)(a/w +t)

  A' = t - sa/w^2

For A' = 0, ...

  w = √(sa/t)

and the height is ...

  a/w = a/√(sa/t) = √(ta/s)

Then the ratio of width to height is ...

  w/(a/w) = w^2/a = (sa/t)/a

  width/height = s/t . . . . . . the premise we started with, above

6 0
3 years ago
A gift box’s rectangular base has a perimeter of 92 centimeters. The length of the base is one more than twice the base’s width.
kozerog [31]
Assume that the length of the rectangle is "l" and that the width is "w".

We are given that: 
(1) The length is one more than twice the base. This means that:
l = 2w + 1 .......> equation I
(2) The perimeter is 92 cm. This means that:
92 = 2(l+w) ...........> equation II

Substitute with equation I in equation II to get the width as follows:
92 = 2(l+w)
92 = 2(2w+1+w)
92/2 = 3w + 1
46 = 3w + 1
3w = 46-1 = 45
w = 45/3
w = 15

Substitute with w in equation I to get the length as follows:
l = 2w + 1 
l = 2(15) + 1
l = 30 + 1 = 31

Based on the above calculations:
length of base = 31 cm
width of base = 15 cm
3 0
3 years ago
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