Question

As part of your exercise routine, you jog around the neighborhood block which is shaped like a right triangle. Your street, the hypotenuse of the triangle, is 850 feet long. If the total distance around your block is 2000 feet, what are the distances of the other two streets that enclose your block?

Answer 1

The other distances are 400 ft and 750 ft.

Explanation:

a + b + c = 2000

a + b + 850 = 2000

a + b = 1150 Equation 1

a^2 + b^2 = c^2

a^2 + b^2 = 850^2

a^2 + b^2 = 722,500 Equation 2

a + b = 1150

a^2 + b^2 = 722,500

a = 1150 - b

(1150 - b)^2 + b^2 = 722,500

1,322,500 - 2300b + b^2 + b^2 = 722,500

2b^2 - 2300b + 600,000 = 0

b^2 - 1150b + 300,000 = 0

`x = (-b \pm √(b^2 - 4ac))/(2a)`

`x = (-(-1150) \pm √((-1150)^2 - 4(1)(300,000)))/(2(1))`

`x = (1150 \pm √(1,322,500 - 1,200,000))/(2)`

`x = (1150 \pm √(122,500))/(2)`

`x = (1150 \pm 350)/(2)`

`x = (1500)/(2)~~~or~~~x = (800)/(2)`

x = 750 or x = 400

Answer: The other distances are 400 ft and 750 ft.