A rectangular flower bed is surrounded by a 1 m wide path and a 26 m2 path area.

| January 17, 2021 | education

A rectangular flower bed is surrounded by a 1 m wide path and a 26 m2 path area. find the sides of the flower bed if one side is 5 m larger than the other.

1. Given a rectangular flower bed.

Let X meters be its width.

It is known that the length of the flower bed is 5 meters longer than the width.

So (X + 5) meters is the width of the flower bed.

The area of ​​the flower bed is X * (X + 5) m2.

2. The problem says that the flower bed is surrounded by a 1 m path on all sides.

Then the side of the rectangle formed by the length of the flower bed and the path is (X + 2) meters.

And the second side is X + 5 + 2 = X + 7 meters.

The area of ​​the rectangle is (X + 2) * (X + 7) m2.

3. Track area 26 m2.

We get the equation.

X * (X + 5) + 26 = (X + 2) * (X + 7).

5 * X + 26 = 9 * X + 14.

4 * X = 12.

X = 3 meters – first side.

3 + 5 = 8 meters – the second.

Answer: The sides of the flower bed are 3 meters and 8 meters.



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