Rational epressions and quadratic functions: A square flower garden is surrounde

Question

Rational epressions and quadratic functions:

A square flower garden is surrounded by a brick walkway that is 1.5 m wide. The area of the walkway is equal to the area of the square flower garden. Determine the dimensions of the flower garden, to the nearest tenth of a metre.

 

 

 

Rational epressions and quadratic functions: A square flower garden is surrounded by a brick walkway that is 1.5 m wide. The area of the walkway is equal to the area of the square flower garden. Determine the dimensions of the flower garden, to the nearest tenth of a metre.

Explanation / Answer

First we need to find the area of the walkway.

Extend the sides of the garden until we get 9 seperate rectangles - the garden, a recangle on each side of the garden, and four squares in the corners.

We know that the area of the garden is its width times its height (w*h = A)

The area of the walkway is the sum of the eight outer rectangles. (2 tall rectangles + 2 wide rectangles + 4 corner squares = A)

The area of a tall rectangle is h * 1.5

The area of a wide rectangle is w * 1.5

The squares will have area 1.5 * 1.5

So, setting the areas equal, we get:

w * h = 2(h * 1.5) + 2(w *1.5) + 4(1.5 *1.5)

We know that the garden is square, so w = h.

See if you can take it from here.

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