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:
[tex]\frac{\text{ new length of a side}}{\text{ original length of a side}}=\frac{30\text{ ft}}{20\text{ ft}}=\frac{3}{2}[/tex]
The perimeter of the new park will be:
[tex]\text{original perimeter}\cdot scale\text{ factor = 136}\cdot\frac{3}{2}=204\text{ ft}[/tex]
Then, the fencing needed to enclose the larger park is:
204 - 136 = 68 ft
The perimeter of the new flower garden will be:
[tex]120\cdot\frac{3}{2}=180\text{ ft}[/tex]
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
