4)
4 is for the Library, 6 is for the park, Police is 5 north up...
Distance of Police from park is by using Pythagoras Theorem:
x^2 = 5^2 + 6^2
x^2 = 25 +36
x^2 = 61 Take the square root of both sides.
x = square root (61) = 7.81.
x = 7.8 miles to the nearest tenth.
5)
Since it is a square garden, let the side be = x.
The length of the fence = x + x +x +x = 4x.
Let length of diagonal = d =34.
By Pythagoras theorem.
x^2 + x^2 = d^2.
2x^2 = 34^2. Divide both sides by 2.
x^2 = (34 *34) / 2 = 17 * 34, Use your calculator.
x^2 = 578. Take square root of both sides.
x = square root (578)
x = 24.04
Total fence = 4x = 4*24.04 = 96.16.
Total fence = 96 feet to the nearest feet.