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What is the length of the Rectangle whose Perimeter is 24 cm and Width is 3 cm?

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  • Last Updated : 20 Nov, 2021

Rectangle is a closed two-dimensional figure composed of four sides and four vertices. All angles of the rectangle are 90 degrees. A rectangle with all sides equal is equivalent to a square. A rectangle is composed of two pairs of parallel sides, length, and width respectively.

Perimeter of Rectangle

The perimeter of a rectangle is the length of the outer boundary of a rectangle. It is also calculated by the summation of the total measure of both the lengths and breadths of the rectangle.

Perimeter of Rectangle Formula

Let us assume a rectangle of perimeter P, whose length and width are ‘l’ and ‘w’ respectively is 2(l + w).

Perimeter of a Rectangle Formula = 2 (Length + Width) units

What is the Length of the Rectangle whose Perimeter is 24 cm and Width is 3 cm?

Solution:

We have, 

Length, l of the rectangle =3 cm

Perimeter of the rectangle, P = 24 cm 

We have, 

Perimeter of a Rectangle Formula = 2 (Length + Width) units

Let us assume w to be the width of rectangle. 

Now, 

P = 2(l + w) cm

Substituting the values, we get, 

P = 2(3 + w) cm

24 = (6 + 2w) cm

On solving, we get, 

18 = 2w 

w = 9 cm

Therefore, the width of rectangle is equivalent to 9 cm. 

Sample Questions

Question 1: Compute the general formula of the width of the rectangle in terms of perimeter P and length l.

Solution: 

Let us assume w to be the width of the rectangle.

We have, 

P = 2(l + w)

P/2 = ( l + w)

On rearranging, we get, 

w = \frac{P}{2} - l

Question 2: Compute the perimeter of the rectangle where length and breadth are 2 and 3 cm respectively.

Solution: 

We know, 

P = 2(l + w)

P = 2 (2 + 3) cm

P = 2 (5) cm

= 10 cm 

Question 3: Compute the length of the rectangle where the perimeter is 20 cm and all sides are equivalent. 

Solution: 

Let us assume s to be the side of the rectangle. 

Now, 

P = 2(l + w)

We know, 

l = w = s

Therefore, 

P = 2(2s)

P = 4s

Substituting, P = 20 cm

s = 20/4 cm 

= 5 cm

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