## 2013/08/13

### Formula Math Perimeter of a Rectangle

Label:
Formula Math

Formula
Math in rectangle, the distance around the outside of the rectangle is
known as perimeter. A rectangle is 2-dimensional; however, perimeter is
1-dimensional and is measured in linear units such as feet or meter
etc.The perimeter of a rectangle is the total length of all the four
sides.

Perimeter of rectangle = 2L + 2W.

Given that:

Perimeter of the rectangle = 2(l + w) units

Thus, the perimeter of the rectangle is 42 cm.

We know that the dimensions of the rectangle in terms of x:

Since the area of a rectangle is given by:

We can substitute the expressions for length and width into the equation for area in order to determine the value of x.

Note that the value of x must be positive and therefore in our case, the value of x is 2. And now we have:

Therefore, the dimensions are 5cm and 3cm.

Now, substituting these values in the formula for perimeter, we will get

Given that:

Area of a rectangle:

Perimeter of a rectangle:

Given that:

Perimeter of rectangle = 2(length + breadth)

Given that:

Length = L = 100m

Width = W = 50m

Rounds = 5

Time per 100m = 5minutes.

Perimeter of the park:

P = 2 L + 2 W.

P = 2 × 100 + 2 × 50

P = 200 + 100

P = 300 m

Total distance walked = 5 × Perimeter of the park.

= 5 × 300

= 1500 meters

Total time taken = Total distance walked × time taken to walk 1m.

= 1500 × 5/100

= 75 minutes or 1hr 15minutes

Perimeter of rectangle = 2L + 2W.

**Math Example 1 :**Rectangle has the length 13 cm and width 8 cm. solve for perimeter of rectangle.*Smart Solution:*Given that:

*Length (l) = 13 cm**Width (w) = 8 cm*Perimeter of the rectangle = 2(l + w) units

*P = 2(13 + 8)**P = 2 (21)**P = 42*Thus, the perimeter of the rectangle is 42 cm.

**Math Example 2:**If a rectangle's length is 2x + 1 and its width is 2x – 1. If its area is 15 cm^{2}, what are the rectangle's dimensions and what is its perimeter?*Smart Solution:*We know that the dimensions of the rectangle in terms of x:

*l = 2x + 1**w = 2x – 1*Since the area of a rectangle is given by:

*A = l * w*We can substitute the expressions for length and width into the equation for area in order to determine the value of x.

*A = l * w**15 = (2x + 1) (2x -1)**15 = 4x*^{2}– 1*16 = 4x*^{2}*x =*±*2*Note that the value of x must be positive and therefore in our case, the value of x is 2. And now we have:

*l = 5 cm**w = 3 cm*Therefore, the dimensions are 5cm and 3cm.

Now, substituting these values in the formula for perimeter, we will get

*P = 2l + 2w**P = 2(5)+2(3)**P = 10+6**P = 16 cm***Math Example 3:**Find the area and the perimeter of a rectangle whose length is 24 m and width is 12m?*Smart Solution:*Given that:

*length = L = 24m**width = W = 12m*Area of a rectangle:

*A = L × W**A = 24 × 12**A = 188 m*^{2}Perimeter of a rectangle:

*P = 2L + 2W**P = 2(24) + 2(12)**P = 48 + 24**P = 72 m***Math Example 4:**Find the area and perimeter of a rectangle whose breadth is 4 cm and the height 3 cm.*Smart Solution:**Area = b×h = 4×3 = 12 cm*^{2}.*Perimeter = 2(b) + 2(h) = 2(4) + 2(3) = 8 + 6 = 14.***Math Example 5:**Calculate the perimeter of the rectangle whose length is 18cm and breadth 7cm*Smart Solution:*Given that:

*L = 18 cm**B = 7 cm*Perimeter of rectangle = 2(length + breadth)

*P = 2 (L + B)**P = 2 (18 + 7)**P = 50 cm***Math Example 6:**Find the perimeter of rectangle whose length is 6 inches and width is 4 inches.*Smart Solution:**P = 2(L + B)**P = 2(6 + 4)**P = 20 in***Math Example 7:**A boy walks 5 times around a park. If the size of the park is 100m by 50m, find the distance the boy has walked. If he walks 100m in 5 minutes, how long will it take for him in total?*Smart Solution:*Given that:

Length = L = 100m

Width = W = 50m

Rounds = 5

Time per 100m = 5minutes.

Perimeter of the park:

P = 2 L + 2 W.

P = 2 × 100 + 2 × 50

P = 200 + 100

P = 300 m

Total distance walked = 5 × Perimeter of the park.

= 5 × 300

= 1500 meters

Total time taken = Total distance walked × time taken to walk 1m.

= 1500 × 5/100

= 75 minutes or 1hr 15minutes

That is smart math formula of Perimeter of a Rectangle

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