Find the area of a rectangleWe know perimeter P=7 m and the length is 4/5 m more than the width

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litteacher8's profile pic

litteacher8 | High School Teacher | (Level 3) Distinguished Educator

Posted on

Sometimes it helps to draw a picture of the rectangle, so you can visualize it.  This way, it won't look just like a formula to you.  Draw a rectangle.  Label two of the sides l and 2 of the sides w.  This should help you picture it.  There are 2 ls and 2 ws, so the formula for perimeter is 2l + 2w = p.  You know p is 7. 

2l + 2w = 7

Snce you know that l is 4/5m more than w, add that to your picture.

Now you can see that making the equation is easy.

2(w+ 4/5) = 7

You can now solve for w.

Distribute:

2w + 8/5 + 2w = 7 (change 8/5 to 1.6)

- 8/5 from both sides

4w = 5.4

Divide both sides by 4

w = 1.35

Now you have w, so you can find l.  Remember

2l + 2w = 7

2l + 2(1.35) = 7

2l + 2.7 = 7

Subtract 2.7

2l = 4.3

divide by 2

l = 2.15

Label your diagram.  Now luckily finding the area is easy.

A = l x w

And you know l and w!

A= 2.15 x 1.35

A= 2.9 (depending on how you round)

See, that wasn't so hard!  When in doubt, draw a diagram!

hala718's profile pic

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

Posted on

We will assume that the length is L and the width is W.

We know that L = 4/5 + w

Also, given that the perimeter p = 7

==> 2L + 2w = 7

We will substitute with L= 4/5 + w

==> 2(4/5 + w) + 2w = 7

==> 8/5 + 2w + 2w = 7

==> 4w = 7- 8/5

==> 4w = 27/5

==> w = 27/20

==> L = 4/5 + 27/20 = 43/20

Now we will calculate the area.

==> A = L*w = 43/20 * 27/20 = 1161/400 = 2.9

==> A = 2.9 m^2

pohnpei397's profile pic

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted on

The area of the rectangle is 2.9 square meters.

We know that the perimeter is 2l + 2w if l is length and w is width.

We know that

l = w + .8

So

2l + 2w = 7

2 (w + .8) + 2w = 7

2w + 1.6 + 2w = 7

4w + 5.4

w = 1.35

So the width is 1.35 and that means the length is 2.15.  So we multiply those two figures together and get 2.9.  (Because area = length times width.)

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll put the width of the rectangle as x and the length as 4/5 + x.

We know that the area of the rectangle is the product of it's dimensions:

A = x*(4/5 + x)

We know that the perimeter is 7 and we know that for finding the perimeter of the rectangle, we'll have to double the sum of it's dimensions.

P = 2(x + 4/5 + x)

P = 4x + 8/5

7 = 4x + 8/5

4x = 7 - 8/5

4x = (35-8)/5

4x = 17/5

x = 17/20

A = (17/20)*(4/5 + 17/20)

A = (17/20)*(33/20)

A = 561/400 square meters

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