math

posted by .

a city block 500ft by 500ft is an unobstructed paved lot, except for a small office building 100ft by 100ft, centered in the middle of the block. What's the shortest distance from the SW corner to the NE corner, going through the paved lot and along (but not through) the building (to the nearest foot)?

  • math -

    The shortest distance from the SW corner of the lot to the NE corner of the lot is along two straight lines which pass through the SE or NW corner of the building.
    If the path passes through the SE corner of the building, the x-displacement is 250+50=300 ft, and the y-displacement is 250-50=200 ft. Find the distance by Pythagoras theorem. Since by symmetry, the other leg has the same length, the total distance is 2√(200²+300²)

  • math -

    The diagonal (c) across the lot:

    500^2 + 500^2 = c^2
    250,000 + 250,000 = 500,000^2
    c = 707.11 feet

    Less the diagonal through the building:

    100^2 + 100^2 = c^2
    10,000 + 10,000 = 20,000^2
    c = 141.43 feet

    707.11 - 141.42 = 565.69 feet

    565.69 + 200 = 765.69 = 766 feet

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Physics

    A room has dimensions 3m(height) X 3.7m X 4.3m. A fly starting at one corner flies arougn, ending up at the diagonally opposite corner. If the fly walks rather than flies what is the lenght of the shortest path it can take?
  2. math

    a developer plans to build a house around a 100ft 10,000 sq ft lake. people want to buy 100ft. how many lots can developer build
  3. algebra 2

    Darla is building a new desk. To make sure she had made a square corner, she measures 4ft. from the corner along one edge and 6ft. from the corner along the other edge. How long (in feet) should the diagonal be between those two points …
  4. algebra 2

    Darla is building a new desk. To make sure she had made a square corner, she measures 10ft from the corner along one edge and 7ft from the corner along the other edge. How long should the diagonal be betwee those two points if the …
  5. math

    a lot owner owns a corner lot , 60mx80m, .find the dimensions x, y of the largest rectangular building he can built pn his lot?
  6. algebra

    Darla is building a new deask. to make sure she had made a square corner, she measures 4ft. from the corner along one edge and 6ft from the corner long the othe edge . how long should the diaonal be between those two points if the …
  7. Physics Please Help

    Two forces, F1 and F2, act on the 5.00 kg block shown in the drawing. The magnitudes of the forces are F1 = 69.0 N and F2 = 24.5 N. What is the horizontal acceleration (magnitude and direction) of the block?
  8. physics

    A 10kg block is released from the top of a ramp 45m high. the track is frictionless except for a 6m stretch in the middle. when the block reaches the end, it compresses the k=2250N/m spring a distance of 0.030m. Find the coefficient …
  9. Physics

    A 10kg block is released from the top of a ramp 45m high. the track is frictionless except for a 6m stretch in the middle. when the block reaches the end, it compresses the k=2250N/m spring a distance of 0.030m. Find the coefficient …
  10. Math

    Darla is building a desk. To make sure she had made a square corner, she measures 7ft from the corner along one edge, and 8ft from the corner of the other edge. How long should the diagonal be between those two points if the corner …

More Similar Questions