Question

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

Answer 1

Dear Student,

Answer: length 20 m and breadth 16 m
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Solution:
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Given half perimeter = 36 m

Perimeter of rectangular garden is 2(x+y) units

here x and y are length and breadth respectively.

Now,According to the question

length is 4 meter more than its width.

let length is x meters than width will be x-4 m

half perimeter = x+y

=
$x + x - 4 = 36 \\ \\ 2x - 4 = 36 \\ \\ 2x = 36 + 4 \\ \\ 2x = 40 \\ \\ x = \frac{40}{2} \\ \\ x = 20$
So, length of rectangular garden is 20 m

breadth is x-4= 20-4 = 16 m

Hope it helps you.

Answer 2

Given : Half of the perimeter = 36 m Let the length of the garden be x m and it's width be y m. Perimeter of rectangular garden =  2(length +width) = 2(x+y)  Perimeter of rectangular garden = 2(x+y) Half of the perimeter = ½ × 2(x+y) = (x + y) m Half of the perimeter = (x + y) m (x + y)  = 36 m …………(1) A.T.Q Length of garden = 4 + width of garden x = 4 + y x - y = 4 ………………(2) On adding eq 1 & 2 x + y  = 36  x - y = 4 ---------------- 2x = 40 x = 40/2 = 20 m Length of garden = 20 m On Putting x = 20 in eq 2 x - y = 4 20 - y = 4 y = 20 - 4 = 16 m y = 16 m  Breadth of garden = 16 m  Hence, the length of rectangular garden is 20 m & Breadth of garden = 16 m  HOPE THIS ANSWER WILL HELP YOU...