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34kurt
3 years ago
11

A rectangular area is formed having a perimeter of 40 cm. Determine the length and breadth of the rectangle if it is to enclose

the maximum possible area​
Mathematics
1 answer:
Vilka [71]3 years ago
5 0

Let x and y be the dimensions of the rectangle. If the perimeter is 40, we have

2(x+y)=40 \iff x+y=20

We can expression one variable in terms of the others as

x+y=20 \iff x=20-y

Since the area is the product of the dimensions, we have

xy=(20-y)y=-y^2+20y

This is a parabola facing down, so it's vertex is the maximum:

f(y)=-y^2+20y \implies f'(y)=-2y+20

So, the maximum is

f'(y)=0 \iff -2y+20=0 \iff 2y=20 \iff y=10

And since we know that x+y=20, we have x=10 as well.

This is actually a well known theorem: out of all the rectangles with given perimeter, the one with the greatest area is the square.

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kolbaska11 [484]
Notice the picture
the rhombus, or kite, is really just 4 triangles
all sides are the same lenght in a rhombus,

thus, find the area of all of the triangles,
and you already have two sides given,
and then, add them up

or just find the length of one, and multiply times 4 :)

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8 0
2 years ago
Find the distance between (3,4) and (4,-6) if necessary, round to the nearest tenth.
Ratling [72]

Answer:

The distance is:

d = 10.0 units (Rounded to the nearest the Tenths Place)

Step-by-step explanation:

Given the points

  • (3,4)
  • (4,-6)

The distance 'd' between (3,4) and (4,-6)

\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):

d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}

substituting the points values

   =\sqrt{\left(4-3\right)^2+\left(-6-4\right)^2}

   =\sqrt{1+10^2}

   =\sqrt{1+100}

   =\sqrt{101}

   =10.0  units (Rounded to the nearest the Tenths Place)

Thus, the distance is:

d = 10.0 units (Rounded to the nearest the Tenths Place)

4 0
3 years ago
200 labourers need 50 days to construct a road of 4 km long. How many labourers are needed to construct 8 km long in 80 days​
patriot [66]

Answer:

250

Step-by-step explanation:

Number of labourers * Number of days worked = Total number of working days

Total number of working days to construct a 4km long road: 200*50=10000

Total mumber of working days to construct a 8km long road: 10000*2=20000

Labourers: 20000 ÷ 80 = 250.

250 labourers are required.

7 0
3 years ago
Por favor me podrían ayudar y dar un ejemplo de cómo llevar a cabo
iogann1982 [59]

Answer:

g

Step-by-step explanation:

7 0
2 years ago
PLEASE HELP QUICKLY IM VERY CONFUSED
Harman [31]

Answer:

42/90

Step-by-step explanation:

               <u>   </u>

Let x = .46

multiply both sides by 10

            <u>    </u>

10x = 4.66

multiply both sides by 10 again

                 <u>    </u>

100x = 46.66

                         <u>    </u>       <u>    </u>

100x - 10x = 46.66 - 4.66

90x = 42

x = 42 / 90

Can be reduced to x = 21/45

7 0
3 years ago
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