Question

a park is in the shape of a rectangle 15 miles long and 8 miles wide. how far do you have to walk if you cut through the park in a diagonal from one comer to the opposite comer? you would walk miles through the park. check answer remaining attempts 3 question 3 a wheelchair ramp is constructed to rise 3 feet off the ground and extends 4 feet along the ground. how long will the wheelchair ramp be? the wheelchair ramp is feet long.

Explanation:

Step1: Apply Pythagorean theorem

For the park problem: Let \(a = 15\) (length), \(b = 8\) (width). The diagonal \(d\) of a rectangle (right - triangle with legs \(a\) and \(b\)) is given by \(d=\sqrt{a^{2}+b^{2}}\). So \(d=\sqrt{15^{2}+8^{2}}=\sqrt{225 + 64}=\sqrt{289}\).
For the ramp problem: Let \(a = 3\) (height), \(b = 4\) (horizontal length). The length \(l\) of the ramp (hypotenuse of a right - triangle) is given by \(l=\sqrt{a^{2}+b^{2}}\). So \(l=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}\).

Answer:

For the park: \(17\) miles.
For the ramp: \(5\) feet.