Answer:
a) TO = OP = 13
b) Height = 12
Explanation:
a) Isosceles triangle TOP with base TP = 10 cm, side TO = OP = x cm.
Perimeter of triangle TOP = 36 cm
=> TO + OP + TP = 36
=> x + x + 10 = 36
=> 2x = 26
=> x = 13
=> TO = OP = 13 cm.
b) Apply Pythagorean theorem:
height^2 + (base/2)^2 = side^2 (height^2 + (TP/2)^2 = TO^2)
or
height^2 + (10/2)^2 = 13^2
or
height^2 + 25 = 169
or
height^2 = 144
or
height = 12
Hope this helps!