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