The plot is rectangular on three sides surrounded by a fence, the total length of which is 170 m.

| May 3, 2021 | education

The plot is rectangular on three sides surrounded by a fence, the total length of which is 170 m. A 40 m long fence has been planted along one of the short sides. What is the area of the plot?

Let a = 40 be the length of the short side of the rectangle.

There are two solutions to this problem, depending on the sum of which sides are taken into account when calculating the length of the fence:

1. The sum of the lengths of the three sides of the rectangle is 2 × a + b = 170m.

We get: 2 × 40 + b = 170;

b = 90.

Formula for the area of a rectangle: S = a × b.

S = 40 × 90 = 3600m2.

2. The sum of the lengths of the three sides of the rectangle is a + 2 × b = 170m.

We get: 40 + 2 × b = 170;

2 × b = 130;

b = 65.

Formula for the area of a rectangle: S = a × b.

S = 40 × 65 = 2600m2.

Answer: 1. 3600m2; 2.2600m2.



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