The rectangular lawn is surrounded by a 30 m long hedge. The area of the lawn is 56m².
May 31, 2021 | education
| 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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