CPM Homework Help : CCA2 Problem 7-21

A semi-circular tunnel is $26$ feet high at its highest point. A road $48$ feet wide is centered under the tunnel. Bruce needs to move a house on a trailer through the tunnel. The load is $22$ feet wide and $24$ feet high. Will he make it? Use a diagram to help justify your reasoning completely.

Hint:

Semi circle, with rectangle inscribed, labeled as follows: top side, 22, right side, 24 with question mark. Line segment passing through the vertical center of rectangle, from base to top point on the semi circle, labeled 26.

Answer:

Added to diagram, diagonal from center bottom, to top right vertex, of rectangle, creating right triangle, labeled as follows: horizontal leg, 11, vertical leg, approximately 23.56, hypotenuse, 26.

If he drives down the center of the road, the height of the tunnel at the edge of the house is only approximately $23.56$ feet. The house will not fit.