Question

Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. The length of the garden is _m.

Answer 1

Hint: Here we go through by the properties of the rectangle. We should apply the formula of perimeter of the rectangle by assuming its width as some variable. By the help of formula we will find out the variable terms.

Complete step-by-step answer:
Let the width of the garden = x meter
Here in the question it is given that length is 4 m more than its width so we can say that,
Then length=(x+4) meter

It is also given that half of the perimeter of the rectangular garden is 36m.
So perimeter of garden$ = (2 \times 36) = 72$meters
As we know that the formula of the perimeter of the rectangle is 2(l+b).
So we can say that,
$ \Rightarrow 2(l + b) = 72$
Now put the value of length and breadth in the formula we get,
$
   \Rightarrow 2(x + x + 4) = 72 \\
   \Rightarrow 2x + 2x + 8 = 72 \\
   \Rightarrow 4x = 64 \\
   \Rightarrow x = 16 \\
 $
Hence, the width of the garden =16 meters
By putting the value of x in length we get the length.
The length of the garden = (16+4) =20 meters

Note: - Whenever you get this type of question the key concept to solve this is to learn the formulas of different shapes like in this case we require the formula of perimeter of rectangle. And when both sides are unknown and the conditions between them are given then assume one side and by that side you will get another side by the given condition.