shortest side ---- x
longer side = 18-x
h^2 = x^2 + (18-x)^2
= 2x^2 - 36x + 324
d(h^2)/dx = 4x - 36
= 0 for a max/min ( for h to be a minimum, h^2 would have to be a minimum) x = 9
when x = 9 , h^2 = 2(81) - 36(9) + 324 = 162
h = √162 or appr 12.728
area = (1/2)(x)(18-x)
= 9x - x^2/2
d(area)/dx = 9 - x/4 = 0 for maximum area
etc.
Q. The sum of the two shortest sides of a right-angles triangle is 18cm.Calculate
a.the least possible length of the hypotenuse
b.the greatest possible area of the triangle
1 answer