Question

A rectangular park is enclosed by picket fencing. The park directorg voted to get so half of the park for a triangular mawer garden. A diagram of the rectangular park and the set as de flower garden is shown below.

Answer 1

The length of the diagonal shown in the picture is computed with help of the Pythagorean theorem, as follows:

c² = a² + b²

c² = 48² + 20²

c² = 2304 + 400

c² = 2704

c = √2704

c = 52 ft

The perimeter of the original flower garden is:

20 + 48 + 52 = 120 ft

The perimeter of the original park is:

2*20 + 2*48 = 136 ft

The scale factor that transforms the original park into the bigger one is:

`\frac{\text{ new length of a side}}{\text{ original length of a side}}=\frac{30\text{ ft}}{20\text{ ft}}=(3)/(2)`

The perimeter of the new park will be:

`\text{original perimeter}\cdot scale\text{ factor = 136}\cdot(3)/(2)=204\text{ ft}`

Then, the fencing needed to enclose the larger park is:

204 - 136 = 68 ft

The perimeter of the new flower garden will be:

`120\cdot(3)/(2)=180\text{ ft}`

From the 68 ft needed to enclose the larger park, 68/2 = 34 ft are used to enclose the larger flower garden. Then, the fencing needed to enclose the larger flower garden is:

180 - 120 - 34 = 26 ft