#### Question

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

#### Solution

Let the length of the garden be x and width of the garden be y.

Then the equation formed are

x = y + 4 ….(1)

Half perimeter = 36

x + y = 36 ….(2)

y = x – 4

x | 0 | 4 |

y | -4 | 0 |

Points | A | B |

y = 36 – x

x | 10 | 20 |

y | 26 | 16 |

Points | C | D |

Plotting these points we draw the lines AB and CD passing through them to represent the equations

The two lines AB and CD intersect at the point (20, 16), So, x = 20 and y = 16 is the required solution of the pair of linear equations i.e. length of the garden is 20 m and width of the garden is 16 m.

**Verification**:

Putting x = 20 and y = 16 in (1). We get

20 = 16 + 4 = 20, (1) is verified.

Putting x = 20 and y = 16 in (2). we get

20 + 16 = 36

36 = 36, (2) is verified.

Hence, both the equations are satisfied