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13 May, 20:25

to find the perimeter of the rectangle you can see the formula P=21+2W. find the perimeter P of a rectangle whose length L is 10 cm and width W is 7 cm.

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  1. 13 May, 21:09
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    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.

    Example 1: Rectangle has the length 13 cm and width 8 cm. solve for perimeter of rectangle.

    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.

    Example 2: If a rectangle's length is 2x + 1 and its width is 2x - 1. If its area is 15 cm2, what are the rectangle's dimensions and what is its perimeter?

    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 = 4x2 - 1

    16 = 4x2

    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

    Example 3: Find the area and the perimeter of a rectangle whose length is 24 m and width is 12m?

    Solution:

    Given that:

    length = L = 24m

    width = W = 12m

    Area of a rectangle:

    A = L * W

    A = 24 * 12

    A = 188 m2

    Perimeter of a rectangle:

    P = 2L + 2W

    P = 2 (24) + 2 (12)

    P = 48 + 24

    P = 72 m

    Example 4: Find the area and perimeter of a rectangle whose breadth is 4 cm and the height 3 cm.

    Solution:

    Area = b*h = 4*3 = 12 cm2.

    Perimeter = 2 (b) + 2 (h) = 2 (4) + 2 (3) = 8 + 6 = 14.

    Example 5: Calculate the perimeter of the rectangle whose length is 18cm and breadth 7cm

    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

    Example 6: Find the perimeter of rectangle whose length is 6 inches and width is 4 inches.

    Solution:

    P = 2 (L + B)

    P = 2 (6 + 4)

    P = 20 in

    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?

    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

    = 75minutes or 1hr 15minutes
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