The perimeter of a rectangular lawn is 80m. If the length had been 2m less and breadth 2m more, the lawn would have been a square. Find the dimensions of the lawn.
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The dimensions of the lawn are 22 m and 18 m

Step-by-step explanation:

Let us solve the question

Let the length of the rectangular lawn is x m and its breadth is y m

∵ The length of the lawn = x meters

∵ The breadth of the lawn = y meters

∵ Its perimeter = 80 meters

→ The formula of the perimeter is P = 2(length + breadth)

∴ 2(Length + breadth) = 80

→ Substitute the length by x and the breadth by y

∴ 2(x + y) = 80

→ Divide both sides by 2

∵ (x + y) = 40

∴ x + y = 40 ⇒ (1)

∵ The length had been 2 m less    

∴ The new length = x - 2 meters

∵ breadth had been 2 m more

∴ The new breadth = y + 2 meters

∵ The lawn would have been a square

→ The square has equal sides, then equate the new length and breadth

∴ x - 2 = y + 2

→ Add 2 to both sides

∵ x - 2 + 2 = y + 2 + 2

∴ x = y + 4 ⇒ (2)

→ Substitute x in equation (1) by equation (2)

∵ y + 4 + y = 40

→ Add the like terms

∴ 2y + 4 = 40

→ Subtract 4 from both sides

∵ 2y + 4 - 4 = 40 - 4

∴ 2y = 36

→ Divide both sides by 2

∴ y = 18

→ Substitute y by 18 in equation (2) to find x

∵ x = 18 + 4

∴ x = 22

∴ The dimensions of the lawn are 22 m and 18 m