Answer:
The dimensions of the lawn are 22 m and 18 m
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