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Alex777 [14]
3 years ago
7

A gardener has three rectangular plots that are adjacent to each other. She has 120 yards of fencing and the total area of the p

lot is 450 square yards, find the dimensions of each plot.
Mathematics
1 answer:
crimeas [40]3 years ago
5 0

Answer:

10 yards by 15 yards

Step-by-step 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 = \frac{150}{y} .......... (4)  

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

3(\frac{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)

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