# The rectangular lawn is surrounded by a 30 m long hedge. The area of the lawn is 56m².

The rectangular lawn is surrounded by a 30 m long hedge. The area of the lawn is 56m². Find the lengths of the sides of the lawn.

1. Take the width of the lawn for x, for the length of the lawn. Let’s make two equations:

x x y = 56;

2 (x + y) = 30; x + y = 15; y = 15 – x.

2. Substitute y = 15 – x in the first equation:

(15 – x) x = 56;

15x – x² – 56 = 0;

x² – 15x + 56 = 0;

The equation has two roots.

The first value x = (15 + √225 – 224) / 2 = (15 + 1) / 2 = 8;

The second value is x = (15 – 1) / 2 = 7.

The width of the lawn can have two values: 7 meters or 8 meters.

The length of the lawn can also have two values: 7 meters or 8 meters.

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