SOLUTION: A unit square is divided into 4 pieces using three cuts as shown. The four pieces can be rearranged to form an isosceles triangle. What is the length of the longest side of the tri

Algebra ->  Pythagorean-theorem -> SOLUTION: A unit square is divided into 4 pieces using three cuts as shown. The four pieces can be rearranged to form an isosceles triangle. What is the length of the longest side of the tri      Log On


   

Question 411572: A unit square is divided into 4 pieces using three cuts as shown. The four pieces can be rearranged to form an isosceles triangle. What is the length of the longest side of the triangle?
It is problem number 18 on http://www.ncssm.edu/smc/tests/Test2009/geo_09.pdf
Please explain how to find the answer.
Answer by sudhanshu_kmr(1152) About Me  (Show Source):
You can put this solution on YOUR website!
Area of unit square = 1 unit sq.
area of triangle is also equal to 1 unit sq.

height of triangle is equal to diagonal of square = 2^(1/2)
for isosceles triangle area = 1/2 * base * height
1= 1/2 * base * height

after solving it...
base = 2^(1/2)

using pythagoras theorem longest side = (5/2)^(1/2)
root(5/2)

correct option is (d) ...