Right triangle with side lengths a, b, c (where c is hypotnuse)
Isosceles means a=b
perimeter = a + b + c = a + a + c
Pythagorean theorem says: a^2 + b^2 = a^2 + a^2 = c^2
You have 2 equations and 2 unknowns. Solve for c.
first draw the triangle. If the hypotenuse is "b" and the 2 other equal sides are "a" then the perimeter is:
You know the angles of an isosceles right triangle, there are 2 45 degree angles and one angle
So the sine of pi over 4 is solve this for "a" and plug that into the original equation for the perimeter and use algebra to solve for "b".