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RSB [31]
3 years ago
15

The perimeter of a rectangle is 36m. If its length is increased by 1m and the width is increased by 2m, its area will increase b

y 30m^2. Find the area of the original rectangle.

Mathematics
1 answer:
maw [93]3 years ago
4 0

Answer:

  80 m^2

Step-by-step explanation:

The given information lets you write two equations involving length (x) and width (y).

  • 2(x +y) = 36 . . . . the perimeter is 36 m
  • (x+1)(y+2) -xy = 30 . . . . increasing the length and width increases area

The second of these equations simplifies to another linear equation, giving a system of linear equations easily solved.

  xy +y +2x + 2 -xy = 30

  2x +y = 28 . . . . . . . subtract 2

Dividing the first equation by 2 gives

  x +y = 18

and subtracting this from the above equation gives ...

  (2x +y) -(x +y) = 28 -18

  x = 10

Then

  y = 18 -10 = 8

The area of the original rectangle is xy = 10·8 = 80 m^2.

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Find the maxmium area of a rectangular plot of land which can be enclosed by rope of length 60 metres​
mario62 [17]

Answer:

225 m²

Step-by-step explanation:

If W is the width of the rectangle, and L is the length, then:

60 = 2W + 2L

A = WL

Use the first equation to solve for one of the variables:

30 = W + L

L = 30 − W

Substitute into the second equation:

A = W (30 − W)

A = 30W − W²

This is a parabola, so we can find the vertex using the formula x = -b/(2a).

W = -30 / (2 × -1)

W = 15

Or, we can use calculus:

dA/dW = 30 − 2W

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Solving for L:

L = 30 − W

L = 15

So the maximum area is:

A = WL

A = (15)(15)

A = 225

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Samantha visits for local farmers market to buy apples and oranges to make a fruit salad. she has $10 to spend. Apples are $.26.
GrogVix [38]
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5 0
3 years ago
Read 2 more answers
Help me please ASAP
uranmaximum [27]

Perimeter is 24.

Length is 4 greater than the width.

Let's use 'x' for width

we can write this as x+4   +   x+4    +    x    +    x

x+4 being the width+4     and    x being the width

There are 4 sides to a rectangle so you are adding 4 values

Two length and two widths

so  we can then combine  the two lengths to make 2x+8

and then combine the two widths to make 2x

Then put it together.       2x+2x+8= 4x+8

4x+8=24

Subtract 8 from both sides

4x=16

divide both sides by 4

x=4

The width is 4.

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False.

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3 years ago
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