# A rectangle has a perimeter of 170 centimeters and a length of 60 centimeters. Find the area.

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**We know that the rectangle has:**

**Perimeter (P) = 170 cm**

**Length (l) = 60 cm**

**Area (A) = lxw = 60xw = ?**

To find the area, we need to find the width. We will find the width using the rectangle's perimeter & length. The formula for perimeter of a rectangle is P= 2(l+w)

- Plug-in what we know: 170 = 2(60+w)
- Divide 2 on both sides: 85 = 60+ w
- Isolate w by subtracting 60 from both sides: 25 = w

Now that we know what w is 25 cm, we can use the area formula and find the area

- A= lxw
- A= 60 cm x 25 cm
- A= 1500 `cm^(2)`

Use the equation 2 ( 60 ) + 2w = 170 with " w " as the width .

2 ( 60 ) + 2w = 170 now multiply 2 with 60 .

By multiplying 2 with 60 , you should get :

120 + 2w = 170 now subtract 120 on both sides

By subtracting 120 on both sides , you should have :

2w = 50 now divide both sides by 2 .

By dividing both sides by 2 , you should get :

w = 25

Since width is 25 and length is 60 , find the area by multiplying 25 with 60

Area = 1500 cm ^2

The perimeter of a rectangle is:

P = 2(w + L), where w is the width and L is the length

From enunciation we know that:

P = 170cm and L = 60cm

We'll substitute P and L by their values:

170cm = 2(w + 60cm)

We'll open the brackets:

170cm = 2w + 120cm

We'll subtract 120cm both sides:

50cm = 2w

We'll divide by 2 both sides:

w = 25cm

Now, knowing the length and the width, we could calculate the area of the rectangle:

A = w*L

A = 25cm*60cm

**A = 1500cm^2**

Given:

Perimeter of rectangle = 170 centimeters

Length of rectangle = 60 centimeters

We know:

Perimeter of rectangle = 2(Length + Width)

Substituting given values of perimeter and length in the above equation:

170 = 2(60 + Width)

170 = 120 + 2*Width

2*Width = 170 - 120 = 50

Therefore:

Width = 50/2 = 25 centimeters

Area of a perimeter is given by:

Area = Length*Width

Substituting the values of Length and width we get:

Area = 60*25 = 1500 centimeter^2

Answer:

Area of Rectangle = 1500 centimeter^2

Perimeter of the rectangle =170 cm. The length is 60cm .

So the breadth of the rectangle = (Primeter- 2*length)/2 = (170-2*60)/2 cm= (170-120)/2 cm= 50/2 cm = 25cm

So the area of the rectangle = length*breadth = 60 cm*25cm = 1500 cm^2