Question

The perimeter of the isosceles right triangle is 2p then it's area

Answer 1

Best Answer:  The ratio of the sides of an isosceles right triangle is:   1 : 1 : √ 2 ,  due to  

the Pythagorean Theorem. The perimeter (P) is:  

 P = 1x + 1x + (√ 2)x = (2 + √ 2)x = 2p ... solve for "x"  

                    x = 2p ⁄ (2 + √ 2)  

 ... where "x" is the scale factor AND in this case it also happens to be the  

 ... length of each of the two identical sides "1x"  

   The area then is:   A = (½) • b • h  

             = (½) • (1x) • (1x)  

             = x² ⁄ 2  ...  replace "x"  

             = [ 2p ⁄ (2 + √ 2)  ]²   ⁄   2  

             = 2p² ⁄ (2 + √ 2)²  

             = 2p² ⁄ (4 + 4√ 2 + 2)  

             = 2p² ⁄ (6 + 4√ 2)  

             = p² ⁄ (3 + 2√ 2) ... area