Find the area of the rectangle whose length is 2 more that twice the width and the perimeter is 22Find the area of the rectangle whose length is 2 more that twice the width and the perimeter is 22

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pohnpei397's profile pic

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

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First, we have to solve for the length and the width.  We can do this by setting up the following equations.

l = 2w + 2

2l + 2w = 22

2 (2w +2) + 2w = 22

4w + 4 + 2w = 22

6w + 4 = 22

6w = 18

w = 3

If w = 3, then the length of the rectangle is 2 more than twice that.  That means that length = 2*3 + 2 or l = 6 + 2 or l = 8

So the width is 3 and the length is 8.  To get the area, we multiply these and we get 24.

So the area is 24.

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Area of the rectangle is:

a = length * width = L*w

But we know that:

L = 2+ 2w

Also:

2L + 2W = 22

Now substitute with L value:

==> 2L + 2W = 22

==> 2(2+2w) + 2w = 22

==> 4 + 4w + 2w = 22

==> 6w = 18

==> w = 3

==> L = 2+ 2*3 = 8

==> a = L*w = 3*8 = 24

==> the area of the rectangle is 24 square unit.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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To calculate the area of the rectangle, we'll have to know the values of the lengths of the sides of the rectangle.

Let's note the length as a and the width as b.

From enunciation we know that:

a = 2 + 2b (1)

From enunciation we also know that the perimeter is 22 units.

The formula for perimeter of a rectangle is:

P = 2(a+b)

22 = 2(a+b)

We'll divide by 2:

a+b = 11 (2)

To calculate a and b we have to solve the system of equations (1) and (2).

We'll substitute (1) in (2):

2 + 2b + b = 11

3b = 11-2

3b = 9

We'll divide by 3:

b = 3

We'll substitute b in (2):

a+3 = 11

a = 11-3

a = 8

Now, we'll calculate the area of the rectangle:

A = a*b

A = 8*3

A = 24 square units

krishna-agrawala's profile pic

krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted on

Let:

Width of rectangle = w = x

Then:

length of rectangle = l = 2x + 2

Perimeter of rectangle = 2(w + l) = 2(x + 2x + 2)= 22

Therefore:

2x + 4x + 4 = 22

6x = 22 - 6 = 18

Therefore:

x = 18/6 = 3

Width = x = 3

Length = 2x + 2

= 2*3 + 2

= 6 + 2 = 8

Area of rectangle = w*l = 3*8 = 24

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

To fibd the area , A .

Area = length*breadth = lb.

Given is the realation: l = 2 more than width or l=2+2b. And Perimeter p = 22.

Algebraically, P = 2(l+b) = 2[(2+2b)+b] = 2(2+3b) =4+6b which should equal to 22  or

4+6b = 22.

6b = 22-4 = 18

6b/6 = 18/6 =3

b = 3.

So by give realtion l = 2+2b , l = 2+2*3 =  8.

So l= 8 and b = 3. Therefore  area A = lb = 8*3 =24

 

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thewriter | College Teacher | (Level 1) Valedictorian

Posted on

Let the length of the rectangle be L and let the width be W.

As the length is 2 more than twice the width: L=2+2W

The perimeter is 22, therefore 2(L+W)=22

=>2(2+2W+W)=22

=>2+3W=11

=>3W=9

=>W=9/3=3

As L=2+2W=2+2*3=8

Therefore the area of the rectangle which is L*W=8*3=24

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