Question

the length of a rectangular gardan is 6 m more than thrice of its breadth. if perimeter is 100 m, find the dimensions of the garden

Answer 1

Let the breadth be x meters

So, the length be (3x + 6) meters

According to Question,

Perimeter of Rectangle = 100 meters

2(length + breadth) = 100 meters

⇒ 2(3x + 6 + x) = 100

⇒ 4x + 6 = 100 / 2

⇒ 4x + 6 = 50

⇒ 4x = 50 - 6

⇒ 4x = 44

⇒ x = 44 / 4

⇒ x = 11

Required Measurements -

Breadth = x = 11 m

Length = 3x + 6 = 3(11) + 6 = 33 + 6

= 39 m

Hence, the length and breadth of the rectangle are 39 meters and 11 meters respectively

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Answer 2

Let us begin by assuming the breadth to be a variable such as ' x '.

Hence,
Breadth of the rectangular garden, b = x m

And according to the question,
Length of the rectangular garden, l = ( 3x + 6 ) m

Also on reading the question further we come to know that,
Perimeter of the rectangular garden = 100 m

Also,
Perimeter of the rectangular garden = 2 ( l + b )

Therefore on relating,
2 ( l + b ) = 100

On substituting the values as assumed earlier,
2 { ( 3x + 6 ) + ( x ) } = 100
3x + 6 + x = 100 / 2
4x + 6 = 50
4x = 50 - 6
4x = 44
x = 44 / 4
x = 11 m

Therefore,

Breadth of the rectangle = x = 11 m
Length of the rectangle = 3x + 6 = 3 * 11 + 6 = 33 + 6 = 39 m

Therefore,

Dimensions of the rectangular garden is 33 m by 11 m.