smc

Question

Point P is taken interior to a square with side-length a and such that is it equally distant from two consecutive vertices and from the side opposite these vertices. If d represents the common distance, then d equals:

Accepted Answer

FIGURE Draw a diagram and label it as shown. Because of SSS Congruency, the two bottom triangles are right triangles. By the Pythagorean Theorem, d^2 = (a-d)^2 + (a2)^2 d^2 = a^2 - 2ad + d^2 + a^24 2ad = 5a^24 d = 5a8 Thus, the answer is 5a8.