Ex 3.1 Q5 - Half the perimeter of a rectangular garden, whose length is 4 m more than its width

Ex 3.1 Q5 - Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.

Solution:-

Let,

      Length of garden = x m

      Width of garden = y m

Case (i): It is given that, length of garden is 4 m more than its width,

   ∴ x = y + 4        ------- ( 1 )

Case (ii): Also given that, half the perimeter of rectangular garden is 36 m,

   ∴

1 / 2

× Perimeter of garden = 36

   ∴

1 / 2

× 2(length + width) = 36

   ∴ x + y = 36

   ∴ y + 4 + y = 36        ------- [ from ( 1 ) ]

   ∴ 2y = 36 - 4

   ∴ 2y = 32

   ∴ y =

32 / 2

   ∴ y = 16

➙ Putting y = 16 in Eqⁿ( 1 )

   ∴ x = 16 + 4

   ∴ x = 20

Therefore,

   *Length of garden

   = x

   = 20 m

   *Width of garden

   = y

   = 16 m

Hence,

        The length and width of the garden is 20 m and 16 m respectively.

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Try This..

✒ The sum of two numbers is 50 and one is 10 more than the other. Find the numbers.

✒ The perimeter of a triangle is 40 cm. One side is 3 cm longer than the second side, and the third side is 5 cm shorter than the second. Find all three sides.

✒ A rectangle’s length is twice its width. If the perimeter is 60 m, find the dimensions.

✒ The sum of two angles is 90°, and one angle is 3 times the other. Find both angles.

❌ Common Mistakes

Not assigning variables correctly:

▸ Always define variables based on what's unknown.

Forgetting units:

▸ Don’t forget to mention meters, centimeters, etc., in your final answer.

Incorrectly interpreting ‘half the perimeter’:

▸ Students often mistake it as half of one side, but it's half the entire perimeter!

Skipping steps:

▸ Always write every step clearly. It helps in avoiding silly errors and also fetches full marks in exams.

Queries Solved:-

Class 10 Ex 3.1

Ex 3.1 Q5 Class 10

Class 10 Ex 3.1 Q5

Class 10 Chap 3 Ex 3.1 Q5

Class 10 Pair Of Linear Equations in Two Variables

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