The length of a rectangle is twice its breadth. If the perimeter is 42cm, find:
1) the length
2) the breath
Let the breadth of rectangle be xm
Length _ 2xm
Perimeter_2 (length + breadth)
Perimeter_ 2 (x+2x)
_ 6x _42m
_3x _21m
On solving we get
x_7m
Breadth_ 7m
Length_ 14m
Area _ length x breadth
_ 14 x 7
Area_ 98 m²
bakwas
first one good
To solve this problem, we will use the information given about the relationship between the length and breadth of the rectangle, as well as the perimeter.
Let's denote the breadth of the rectangle as 'b'.
1) Finding the length:
According to the given information, the length of the rectangle is twice its breadth. So, the length can be expressed as '2b'.
2) Finding the breadth:
The perimeter of a rectangle is the sum of the lengths of all its sides. For this rectangle, the perimeter is given as 42 cm. Since a rectangle has two pairs of equal sides, we can express the perimeter as:
Perimeter = 2 × (Length + Breadth)
Substituting the values we found earlier:
42 = 2 × (2b + b)
Now, let's solve this equation to find the value of 'b'.
42 = 2 × (3b)
Divide both sides of the equation by 2 to isolate the expression:
21 = 3b
Divide both sides of the equation by 3 to solve for 'b':
b = 7 cm
Now that we have found the value of 'b', we can substitute it back into the expression for the length to find the value of the length.
Length = 2b = 2 × 7 = 14 cm
Therefore, the length of the rectangle is 14 cm and the breadth is 7 cm.
P = 2L + 2W
42 = 2(2W) + 2W
42 = 6W
7 = W