Question

A gardener has three rectangular plots that are adjacent to each other. She has 120 yards of fencing and the total area of the plot is 450 square yards, find the dimensions of each plot.

Answer 1

10 yards by 15 yards

Explanation:

Let the dimensions of each plot x yards by y yards.

If three plots are placed as the y-yards side are common to them then,

The total perimeter will be (6x + 4y) = P = 120 yards {Given} ........... (1)

⇒ 3x + 2y = 60 ........... (2)

Now, the total area of the three plots will be 3xy = A = 450 sq, yards {Given} .......... (3)

⇒
`x = (150)/(y)` .......... (4)

Now, solving equations (2) and (4) we get,

`3((150)/(y)) + 2y = 60`

⇒ 225 + y² = 30y

⇒ y² - 30y + 225 = 0

⇒ (y - 15)² = 0

⇒ y = 15 yards.

Hence, from equation (4) we get,

x = 150/15 = 10 yards.

Therefore, the dimensions of each plot are 10 yards by 15 yards. (Answer)